US11126761B2 - Free energy calculation device, method, program, and recording medium with the program recorded thereon - Google Patents
Free energy calculation device, method, program, and recording medium with the program recorded thereon Download PDFInfo
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- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
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- G16B5/00—ICT specially adapted for modelling or simulations in systems biology, e.g. gene-regulatory networks, protein interaction networks or metabolic networks
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Definitions
- This disclosure relates to a device, a method, a program, and a recording medium with the program recorded thereon, for calculating a difference in free energy between different molecules at a high speed with a high accuracy.
- binding affinity prediction by calculating a difference in binding free energy between the protein and different ligands for the protein using computer simulation such as a molecular dynamics method or a Monte Carlo method.
- the binding free energy between a protein and a ligand is a physical quantity strictly correlated with a binding constant as an indicative of binding affinity between the protein and the ligand.
- a difference in binding free energy between different ligands for the same protein is a physical quantity strictly correlated with a ratio of binding constants between the different ligands and the protein.
- a difference in binding affinity between different ligands for the same protein can be determined by a difference in binding free energy. That is, if it is possible to calculate a difference in binding free energy between different ligands for the same protein at a high speed with a high accuracy, prior to synthesis of a ligand and a binding strength experiment, by changing a functional group of the ligand and a backbone structure thereof, a molecular structure of the ligand can be designed such that binding free energy between a protein and a ligand is reduced, and acceleration and higher efficiency in drug discovery and development can be expected.
- drug discovery and development require a free energy calculation method having a high speed at a level capable of calculating in practical calculation time of a few days or less, and having a high accuracy at a level capable of reproducing binding free energy or a difference in binding free energy obtained by a binding affinity experiment in an average error of ⁇ 1 kcal/mol or less.
- Examples of a representative free energy calculation method include the free energy perturbation method (The Journal of Chemical Physics, 22(8), 1420-1426 (1954)), the particle insertion method (The Journal of Chemical Physics, 39(11), 2808-2812 (1963)), and the energy representation method (The Journal of Chemical Physics, 113(15), 6070-6081 (2000), The Journal of Chemical Physics, 117(8), 3605-3616 (2002) and The Journal of Chemical Physics, 119(18), 9686-9702 (2003)).
- the free energy perturbation method is a calculation method of determining a difference in free energy between an initial state of a calculation target and a final state of a calculation target by gradually changing parameters for an intermolecular interaction between a ligand and a surrounding environment of the ligand such as water or a protein, introducing many virtual intermediate states connecting an initial state of a calculation target and a final state thereof, and determining and summing a difference in free energy between adjacent states.
- the free energy perturbation method can reproduce a difference in binding free energy between different ligands for the same protein obtained by a binding affinity experiment with a high accuracy.
- the free energy perturbation method requires a long computing time, and is not a practical calculation method disadvantageously.
- the particle insertion method is a method not requiring introduction of an intermediate state between an initial state containing no ligand but constituted by a solvent, a protein, or the like and a final state in which a ligand is bound to a protein to form a complex when binding free energy is calculated.
- the particle insertion method includes a step of generating many final states by repeating a sampling step of selecting position coordinates at random in an initial state and adding a ligand to the position coordinates.
- a ligand interacts with a specific amino acid residue constituting a protein in a specific active site of a protein, and forms a complex in which the ligand and the protein are bound to each other.
- the energy representation method has a calculation accuracy almost equal to the free energy perturbation method, and is a method capable of calculating free energy at a high speed.
- the energy representation method includes a step of generating many final states constituted by a complex in which a ligand is bound to a protein and a solvent by repeating a sampling step of selecting position coordinates at random in an initial state containing no ligand but constituted by a solvent, a protein or the like and adding a ligand to the position coordinates. Therefore, binding free energy cannot be calculated.
- the free energy perturbation method needs to introduce many intermediate states connecting an initial state and a final state, and has a long calculation time disadvantageously.
- the particle insertion method or the energy representation method requiring to introduce no intermediate states, it is impossible to generate many complexes in which a ligand and a protein are bound to each other by adding the ligand to randomly selected position coordinates in an initial state containing no ligand but constituted by a solvent, a protein or the like, and binding free energy cannot be calculated disadvantageously. Therefore, it could be helpful is to provide a device, a method, a program, and a recording medium with the program recorded thereon, for calculating a difference in free energy between different molecules at a high speed with a high accuracy.
- A represents an atomic assembly consisting of structure a or containing structure a
- B represents a fragment consisting of one or more atoms
- AB represents an atomic assembly consisting of atomic assembly A and fragment B connected to structure a of the atomic assembly A
- control unit includes:
- a first atomic assembly model creation unit for creating a first atomic assembly model modeling atomic assembly A before the change
- a first coordinates acquisition unit for acquiring coordinates of atomic assembly A in each of first to i th states F 1 to F i (wherein i is an integer of two or more) by computer simulation with respect to the first atomic assembly model created by the first atomic assembly model creation unit;
- a second coordinates acquisition unit for acquiring coordinates of atomic assembly AB generated by connection of fragment B to atomic assembly A in each of states F 1 to F i based on the coordinates of atomic assembly A acquired by the first coordinates acquisition unit;
- a first interaction energy ⁇ frequency distribution creation unit for calculating interaction energy ⁇ between structure a and fragment B connected to the structure a based on the coordinates of atomic assembly AB acquired by the second coordinates acquisition unit, and creating a frequency distribution indicating a frequency in each class of interaction energy ⁇ ;
- a first interaction energy ⁇ appearance probability calculation unit for calculating an appearance probability P 0 ( ⁇ ) in each class of interaction energy ⁇ based on the frequency distribution created by the first interaction energy ⁇ frequency distribution creation unit;
- a first interaction energy ⁇ frequency distribution creation unit for calculating interaction energy ⁇ between a part or the whole of an atomic assembly generated by removing structure aB consisting of structure a and fragment B connected to the structure a from atomic assembly AB, and fragment B based on the coordinates of atomic assembly AB acquired by the second coordinates acquisition unit, and creating a frequency distribution indicating a frequency in each class of interaction energy ⁇ in each class of interaction energy ⁇ in the frequency distribution created by the first interaction energy ⁇ frequency distribution creation unit;
- a first interaction energy ⁇ appearance probability calculation unit for calculating an appearance probability P 0 ′( ⁇ ; ⁇ ) in each class of interaction energy ⁇ in each class of interaction energy ⁇ based on the frequency distribution created by the first interaction energy ⁇ frequency distribution creation unit;
- a second atomic assembly model creation unit for creating a second atomic assembly model modeling atomic assembly AB after the change
- a third coordinates acquisition unit for acquiring coordinates of atomic assembly AB in each of first to j th states G 1 to G j (wherein j is an integer of two or more) by computer simulation with respect to the second atomic assembly model created by the second atomic assembly model creation unit;
- a second interaction energy ⁇ frequency distribution creation unit for calculating interaction energy ⁇ between structure a and fragment B connected to the structure a based on the coordinates of atomic assembly AB acquired by the third coordinates acquisition unit, and creating a frequency distribution indicating a frequency in each class of interaction energy ⁇ ;
- a second interaction energy ⁇ appearance probability calculation unit for calculating an appearance probability P( ⁇ ) in each class of interaction energy ⁇ based on the frequency distribution created by the second interaction energy ⁇ frequency distribution creation unit;
- a second interaction energy ⁇ frequency distribution creation unit for calculating interaction energy ⁇ between a part or the whole of an atomic assembly generated by removing structure aB consisting of structure a and fragment B connected to the structure a from atomic assembly AB, and fragment B based on the coordinates of atomic assembly AB acquired by the third coordinates acquisition unit, and creating a frequency distribution indicating a frequency in each class of interaction energy ⁇ ;
- a second interaction energy ⁇ appearance probability calculation unit for calculating an appearance probability P′( ⁇ ) in each class of interaction energy ⁇ based on the frequency distribution created by the second interaction energy ⁇ frequency distribution creation unit;
- a ⁇ ( ⁇ )P( ⁇ )d ⁇ calculation unit for calculating a free energy change amount ⁇ ( ⁇ )P( ⁇ )d ⁇ , wherein ⁇ ( ⁇ ) represents a free energy change amount caused by interaction energy ⁇ in each class of interaction energy ⁇ , caused by interaction energy ⁇ based on P( ⁇ ) calculated by the second interaction energy ⁇ appearance probability calculation unit, P 0 ′( ⁇ ; ⁇ ) calculated by the first interaction energy ⁇ appearance probability calculation unit, and P′( ⁇ ) calculated by the second interaction energy ⁇ appearance probability calculation unit; and
- a ⁇ G calculation unit for calculating ⁇ G based on P 0 ( ⁇ ) calculated by the first interaction energy ⁇ appearance probability calculation unit, P( ⁇ ) calculated by the second interaction energy ⁇ appearance probability calculation unit, ⁇ ( ⁇ )P( ⁇ )d ⁇ calculated by the ⁇ ( ⁇ )P( ⁇ )d ⁇ calculation unit, and numerical formula (1):
- ⁇ ⁇ ⁇ G ⁇ ⁇ ⁇ ⁇ P ⁇ ( ⁇ ) ⁇ d ⁇ ⁇ ⁇ + RT ⁇ ⁇ P ⁇ ( ⁇ ) ⁇ log ⁇ ( P ⁇ ( ⁇ ) P 0 ⁇ ( ⁇ ) ) ⁇ d ⁇ ⁇ ⁇ + ⁇ ⁇ ⁇ ⁇ v ⁇ ( ⁇ ) ⁇ P ⁇ ( ⁇ ) ⁇ d ⁇ ⁇ ⁇ ( 1 )
- R represents a gas constant
- T represents an absolute temperature at which the change represented by reaction formula (1) occurs.
- the second coordinates acquisition unit In an aspect of the calculation device (hereinafter, referred to as “aspect 1A”), the second coordinates acquisition unit
- a selected atomic group consisting of one or more atoms selected from atoms constituting structure a, rotates and/or translates coordinates of a selected atomic group of atomic assembly C in one or more states selected from states H 1 to H k with respect to coordinates of a selected atomic group of atomic assembly A in each of states F 1 to F i , thereby creates coordinates of atomic assembly C having the minimum sum of squares of distances between corresponding atoms between the selected atomic group of atomic assembly A and the selected atomic group of atomic assembly C, superimposes atomic assembly C in one or more states selected from states H 1 to H k on atomic assembly A based on the created coordinates of atomic assembly C, and acquires one or more coordinates of atomic assembly AB generated by connection of fragment B to atomic assembly A based on coordinates of atomic assembly A and one or more coordinates of fragment B of atomic assembly C superimposed on atomic assembly A.
- the ⁇ ( ⁇ )P( ⁇ )d ⁇ calculation unit calculates a free energy change amount ⁇ ( ⁇ )P( ⁇ )d ⁇ caused by interaction energy ⁇ based on P( ⁇ ) calculated by the second interaction energy ⁇ appearance probability calculation unit, P 0 ′( ⁇ ; ⁇ ) calculated by the first interaction energy ⁇ appearance probability calculation unit, and P′( ⁇ ) calculated by the second interaction energy ⁇ appearance probability calculation unit by the energy representation method.
- fragment B is constituted by an atom(s) containing a point charge(s) as a virtual atom(s), and the second coordinates acquisition unit adds the point charge(s) of fragment B to a charge parameter(s) of an atom(s) constituting structure a of atomic assembly A.
- Two or more of the aspects 1A to 3A can be combined.
- reaction formula (1) A+B ⁇ AB (1)
- A represents an atomic assembly consisting of structure a or containing structure a
- B represents a fragment consisting of one or more atoms
- AB represents an atomic assembly consisting of atomic assembly A and fragment B connected to structure a of the atomic assembly A
- a control unit of the computer performs:
- a first atomic assembly model creation step for creating a first atomic assembly model modeling atomic assembly A before the change
- a first coordinates acquisition step for acquiring coordinates of atomic assembly A in each of first to i th states F 1 to F i (wherein i is an integer of two or more) by computer simulation with respect to the first atomic assembly model created by the first atomic assembly model creation step;
- a second coordinates acquisition step for acquiring coordinates of atomic assembly AB generated by connection of fragment B to atomic assembly A in each of states F 1 to F i based on the coordinates of atomic assembly A acquired by the first coordinates acquisition step;
- a first interaction energy ⁇ frequency distribution creation step for calculating interaction energy ⁇ between structure a and fragment B connected to the structure a based on the coordinates of atomic assembly AB acquired by the second coordinates acquisition step, and creating a frequency distribution indicating a frequency in each class of interaction energy ⁇ ;
- a first interaction energy ⁇ appearance probability calculation step for calculating an appearance probability P 0 ( ⁇ ) in each class of interaction energy ⁇ based on the frequency distribution created by the first interaction energy ⁇ frequency distribution creation step;
- a first interaction energy ⁇ frequency distribution creation step for calculating interaction energy ⁇ between a part or the whole of an atomic assembly generated by removing structure aB consisting of structure a and fragment B connected to the structure a from atomic assembly AB, and fragment B based on the coordinates of atomic assembly AB acquired by the second coordinates acquisition step, and creating a frequency distribution indicating a frequency in each class of interaction energy ⁇ in each class of interaction energy ⁇ in the frequency distribution created by the first interaction energy ⁇ frequency distribution creation step;
- a first interaction energy ⁇ appearance probability calculation step for calculating an appearance probability P 0 ′( ⁇ ; ⁇ ) in each class of interaction energy ⁇ in each class of interaction energy ⁇ based on the frequency distribution created by the first interaction energy ⁇ frequency distribution creation step;
- a second atomic assembly model creation step for creating a second atomic assembly model modeling atomic assembly AB after the change
- a third coordinates acquisition step for acquiring coordinates of atomic assembly AB in each of first to j th states G 1 to G j (wherein j is an integer of two or more) by computer simulation with respect to the second atomic assembly model created by the second atomic assembly model creation step;
- a second interaction energy ⁇ frequency distribution creation step for calculating interaction energy ⁇ between structure a and fragment B connected to the structure a based on the coordinates of atomic assembly AB acquired by the third coordinates acquisition step, and creating a frequency distribution indicating a frequency in each class of interaction energy ⁇ ;
- a second interaction energy ⁇ appearance probability calculation step for calculating an appearance probability P( ⁇ ) in each class of interaction energy ⁇ based on the frequency distribution created by the second interaction energy ⁇ frequency distribution creation step;
- a second interaction energy ⁇ frequency distribution creation step for calculating interaction energy ⁇ between a part or the whole of an atomic assembly generated by removing structure aB consisting of structure a and fragment B connected to the structure a from atomic assembly AB, and fragment B based on the coordinates of atomic assembly AB acquired by the third coordinates acquisition step, and creating a frequency distribution indicating a frequency in each class of interaction energy ⁇ ;
- a second interaction energy ⁇ appearance probability calculation step for calculating an appearance probability P′( ⁇ ) in each class of interaction energy ⁇ based on the frequency distribution created by the second interaction energy ⁇ frequency distribution creation step;
- a ⁇ ( ⁇ )P( ⁇ )d ⁇ calculation step for calculating a free energy change amount ⁇ ( ⁇ )P( ⁇ )d ⁇ , wherein ⁇ ( ⁇ ) represents a free energy change amount caused by interaction energy ⁇ in each class of interaction energy ⁇ , caused by interaction energy ⁇ based on P( ⁇ ) calculated by the second interaction energy ⁇ appearance probability calculation step, P 0 ′( ⁇ ; ⁇ ) calculated by the first interaction energy ⁇ appearance probability calculation step, and P′( ⁇ ) calculated by the second interaction energy ⁇ appearance probability calculation step; and
- a ⁇ G calculation step for calculating ⁇ G based on P 0 ( ⁇ ) calculated by the first interaction energy ⁇ appearance probability calculation step, P( ⁇ ) calculated by the second interaction energy ⁇ appearance probability calculation step, ⁇ ( ⁇ )P( ⁇ )d ⁇ calculated by the ⁇ ( ⁇ )P( ⁇ )d ⁇ calculation step, and numerical formula (1):
- ⁇ ⁇ ⁇ G ⁇ ⁇ ⁇ ⁇ P ⁇ ( ⁇ ) ⁇ d ⁇ ⁇ ⁇ + RT ⁇ ⁇ P ⁇ ( ⁇ ) ⁇ log ⁇ ( P ⁇ ( ⁇ ) P 0 ⁇ ( ⁇ ) ) ⁇ d ⁇ ⁇ ⁇ + ⁇ ⁇ ⁇ ⁇ v ⁇ ( ⁇ ) ⁇ P ⁇ ( ⁇ ) ⁇ d ⁇ ⁇ ⁇ ( 1 )
- R represents a gas constant
- T represents an absolute temperature at which the change represented by reaction formula (1) occurs.
- a selected atomic group consisting of one or more atoms selected from atoms constituting structure a, rotates and/or translates coordinates of a selected atomic group of atomic assembly C in one or more states selected from states H 1 to H k with respect to coordinates of a selected atomic group of atomic assembly A in each of states F 1 to F i , thereby creates coordinates of atomic assembly C having the minimum sum of squares of distances between corresponding atoms between the selected atomic group of atomic assembly A and the selected atomic group of atomic assembly C, superimposes atomic assembly C in one or more states selected from states H 1 to H k on atomic assembly A based on the created coordinates of atomic assembly C, and acquires one or more coordinates of atomic assembly AB generated by connection of fragment B to atomic assembly A based on coordinates of atomic assembly A and one or more coordinates of fragment B of atomic assembly C superimposed on atomic assembly A.
- the control unit of the computer calculates a free energy change amount ⁇ ( ⁇ )P( ⁇ )d ⁇ caused by interaction energy ⁇ based on P( ⁇ ) calculated by the second interaction energy ⁇ appearance probability calculation step, P 0 ′( ⁇ ; ⁇ ) calculated by the first interaction energy ⁇ appearance probability calculation step, and P′( ⁇ ) calculated by the second interaction energy ⁇ appearance probability calculation step by the energy representation method.
- fragment B is constituted of an atom(s) containing a point charge(s) as a virtual atom(s), and in the second coordinates acquisition step, the control unit of the computer adds the point charge(s) of fragment B to a charge parameter(s) of an atom(s) constituting structure a of atomic assembly A.
- reaction formula (1) A+B ⁇ AB (1)
- A represents an atomic assembly consisting of structure a or containing structure a
- B represents a fragment consisting of one or more atoms
- AB represents an atomic assembly consisting of atomic assembly A and fragment B connected to structure a of the atomic assembly A
- control unit of a computer causes a control unit of a computer to function as:
- a first atomic assembly model creation unit for creating a first atomic assembly model modeling atomic assembly A before the change
- a first coordinates acquisition unit for acquiring coordinates of atomic assembly A in each of first to i th states F 1 to F i (wherein i is an integer of two or more) by computer simulation with respect to the first atomic assembly model created by the first atomic assembly model creation unit;
- a second coordinates acquisition unit for acquiring coordinates of atomic assembly AB generated by connection of fragment B to atomic assembly A in each of states F 1 to F i based on the coordinates of atomic assembly A acquired by the first coordinates acquisition unit;
- a first interaction energy ⁇ frequency distribution creation unit for calculating interaction energy ⁇ between structure a and fragment B connected to the structure a based on the coordinates of atomic assembly AB acquired by the second coordinates acquisition unit, and creating a frequency distribution indicating a frequency in each class of interaction energy ⁇ ;
- a first interaction energy ⁇ appearance probability calculation unit for calculating an appearance probability P 0 ( ⁇ ) in each class of interaction energy ⁇ based on the frequency distribution created by the first interaction energy ⁇ frequency distribution creation unit;
- a first interaction energy ⁇ frequency distribution creation unit for calculating interaction energy ⁇ between a part or the whole of an atomic assembly generated by removing structure aB consisting of structure a and fragment B connected to the structure a from atomic assembly AB, and fragment B based on the coordinates of atomic assembly AB acquired by the second coordinates acquisition unit, and creating a frequency distribution indicating a frequency in each class of interaction energy ⁇ in each class of interaction energy ⁇ in the frequency distribution created by the first interaction energy ⁇ frequency distribution creation unit;
- a first interaction energy ⁇ appearance probability calculation unit for calculating an appearance probability P 0 ′( ⁇ ; ⁇ ) in each class of interaction energy ⁇ in each class of interaction energy ⁇ based on the frequency distribution created by the first interaction energy ⁇ frequency distribution creation unit;
- a second atomic assembly model creation unit for creating a second atomic assembly model modeling atomic assembly AB after the change
- a third coordinates acquisition unit for acquiring coordinates of atomic assembly AB in each of first to j th states G 1 to G j (wherein j is an integer of two or more) by computer simulation with respect to the second atomic assembly model created by the second atomic assembly model creation unit;
- a second interaction energy ⁇ frequency distribution creation unit for calculating interaction energy ⁇ between structure a and fragment B connected to the structure a based on the coordinates of atomic assembly AB acquired by the third coordinates acquisition unit, and creating a frequency distribution indicating a frequency in each class of interaction energy ⁇ ;
- a second interaction energy ⁇ appearance probability calculation unit for calculating an appearance probability P( ⁇ ) in each class of interaction energy ⁇ based on the frequency distribution created by the second interaction energy ⁇ frequency distribution creation unit;
- a second interaction energy ⁇ frequency distribution creation unit for calculating interaction energy ⁇ between a part or the whole of an atomic assembly generated by removing structure aB consisting of structure a and fragment B connected to the structure a from atomic assembly AB, and fragment B based on the coordinates of atomic assembly AB acquired by the third coordinates acquisition unit, and creating a frequency distribution indicating a frequency in each class of interaction energy ⁇ ;
- a second interaction energy ⁇ appearance probability calculation unit for calculating an appearance probability P′( ⁇ ) in each class of interaction energy ⁇ based on the frequency distribution created by the second interaction energy ⁇ frequency distribution creation unit;
- a ⁇ ( ⁇ )P( ⁇ )d ⁇ calculation unit for calculating a free energy change amount ⁇ ( ⁇ )P( ⁇ )d ⁇ , wherein ⁇ ( ⁇ ) represents a free energy change amount caused by interaction energy ⁇ in each class of interaction energy ⁇ , caused by interaction energy ⁇ based on P( ⁇ ) calculated by the second interaction energy ⁇ appearance probability calculation unit, P 0 ′( ⁇ ; ⁇ ) calculated by the first interaction energy ⁇ appearance probability calculation unit, and P′( ⁇ ) calculated by the second interaction energy ⁇ appearance probability calculation unit; and
- a ⁇ G calculation unit for calculating ⁇ G based on P 0 ( ⁇ ) calculated by the first interaction energy ⁇ appearance probability calculation unit, P( ⁇ ) calculated by the second interaction energy ⁇ appearance probability calculation unit, ⁇ ( ⁇ )P( ⁇ )d ⁇ calculated by the ⁇ ( ⁇ )P( ⁇ )d ⁇ calculation unit, and numerical formula (1):
- ⁇ ⁇ ⁇ G ⁇ ⁇ ⁇ ⁇ P ⁇ ( ⁇ ) ⁇ d ⁇ ⁇ ⁇ + RT ⁇ ⁇ P ⁇ ( ⁇ ) ⁇ log ⁇ ( P ⁇ ( ⁇ ) P 0 ⁇ ( ⁇ ) ) ⁇ d ⁇ ⁇ ⁇ + ⁇ ⁇ ⁇ ⁇ v ⁇ ( ⁇ ) ⁇ P ⁇ ( ⁇ ) ⁇ d ⁇ ⁇ ⁇ ( 1 )
- R represents a gas constant
- T represents an absolute temperature at which the change represented by reaction formula (1) occurs.
- the second coordinates acquisition unit In an aspect of the program (hereinafter, referred to as “aspect 1C”), the second coordinates acquisition unit
- a selected atomic group consisting of one or more atoms selected from atoms constituting structure a, rotates and/or translates coordinates of a selected atomic group of atomic assembly C in one or more states selected from states H 1 to H k with respect to coordinates of a selected atomic group of atomic assembly A in each of states F 1 to F i , thereby creates coordinates of atomic assembly C having the minimum sum of squares of distances between corresponding atoms between the selected atomic group of atomic assembly A and the selected atomic group of atomic assembly C, superimposes atomic assembly C in one or more states selected from states H 1 to H k on atomic assembly A based on the created coordinates of atomic assembly C, and acquires one or more coordinates of atomic assembly AB generated by connection of fragment B to atomic assembly A based on coordinates of atomic assembly A and one or more coordinates of fragment B of atomic assembly C superimposed on atomic assembly A.
- the ⁇ ( ⁇ )P( ⁇ )d ⁇ calculation unit calculates a free energy change amount ⁇ ( ⁇ )P( ⁇ )d ⁇ caused by interaction energy ⁇ based on P( ⁇ ) calculated by the second interaction energy ⁇ appearance probability calculation unit, P 0 ′( ⁇ ; ⁇ ) calculated by the first interaction energy ⁇ appearance probability calculation unit, and P′( ⁇ ) calculated by the second interaction energy ⁇ appearance probability calculation unit by the energy representation method.
- fragment B is constituted by an atom(s) containing a point charge(s) as a virtual atom(s), and the second coordinates acquisition unit adds the point charge(s) of fragment B to a charge parameter(s) of an atom(s) constituting structure a of atomic assembly A.
- coordinates of atomic assembly AB can be acquired efficiently. This can improve a sampling efficiency from an ensemble generated by computer simulation significantly as compared with the particle insertion method or the energy representation method. In addition, improvement of the sampling efficiency makes it possible to calculate numerical formula (1) satisfying a classical statistical mechanics theory with a statistically correct accuracy, and makes it possible to secure a high calculation accuracy. Furthermore, an intermediate state connecting an initial state and a final state is not required. Therefore, calculation time can be reduced largely as compared with the free energy perturbation method. Therefore, a difference in binding free energy between different molecules can be calculated at a high speed with a high accuracy, and acceleration and higher efficiency in novel drug discovery and development are possible.
- FIG. 1 is a functional block diagram illustrating a configuration of a calculation device according to an example.
- FIG. 2 is a flowchart illustrating a processing procedure of the calculation device according to the example.
- FIG. 3 is a flowchart illustrating an example of a processing procedure in step S 120 .
- FIG. 4 is a flowchart illustrating an example of a processing procedure in step S 130 .
- FIG. 5 is a flowchart illustrating another example of a processing procedure in step S 130 .
- FIG. 6 is a flowchart illustrating an example of a processing procedure in step S 220 .
- reaction formula (1) a difference between the sum of free energy of an atomic assembly A before the change and free energy of a fragment B, and free energy of an atomic assembly AB after the change is represented by numerical formula (2).
- an integral sign ( ⁇ ) represents an integral sign for each integration variable collectively.
- P( ⁇ ) that is an appearance probability (that is, an energy distribution) of interaction energy ⁇ between structure a in atomic assembly AB after the change and fragment B connected to the structure a is represented by numerical formula (3).
- P 0 ( ⁇ ) that is an appearance probability (that is, an energy distribution) of interaction energy ⁇ between structure a in atomic assembly AB generated by connection of fragment B to atomic assembly A before the change and fragment B connected to the structure a is represented by numerical formula (4).
- a ratio therebetween can be represented by numerical formula (5).
- Numerical formula (1) can be introduced by modifying numerical formula (5).
- ⁇ ( ⁇ ( ⁇ ( ⁇ , K ) ⁇ ( ⁇ ) ⁇ W ( K ))) is a delta function of Dirac, and is a function to obtain 1 when ⁇ is equal to ⁇ ( ⁇ , K ) ⁇ ( ⁇ ) ⁇ W ( K ) and to obtain zero when ⁇ is not equal thereto.
- X set of coordinates of all the atoms constituting atomic assembly generated by removing structure aB consisting of structure a and fragment B connected to the structure a from atomic assembly AB after change (that is, environment around structure aB in atomic assembly AB after change) or set of coordinates of all the atoms constituting atomic assembly generated by removing structure a from atomic assembly A before change (that is, environment around structure a in atomic assembly A before change)
- x i set of coordinates of i th molecule constituting atomic assembly (for example, set of coordinates of atoms constituting i th water molecule in a case where atomic assembly AB contains a plurality of water molecules and the number is given to each of the water molecules) in atomic assembly generated by removing structure aB consisting of structure a and fragment B connected to the structure a from atomic assembly AB after change (that is, environment around structure aB in atomic assembly AB after change) or atomic assembly generated by removing structure a from atomic assembly A before change (that is, environment around structure a in atomic assembly A before change)
- ⁇ interaction energy between atoms constituting structure aB consisting of structure a and fragment B connected to the structure a
- ⁇ interaction energy between structure aB consisting of structure a and fragment B connected to the structure a and environment around the structure aB (that is, atomic assembly generated by removing the structure aB from atomic assembly AB) in atomic assembly AB after change
- Interaction energy in ⁇ , ⁇ , W, U, ⁇ , and u means energy caused by interaction for interatomic bond involving a bond length, a bond angle, a twist angle, or the like, and energy caused by non-bonding interaction such as van der Waals interaction or electrostatic interaction or the like.
- the first term of numerical formula (1) represents an average value of interaction energy ⁇ between structure a in atomic assembly AB after the change and fragment B connected to the structure a.
- the first and second terms in numerical formula (1) represent a free energy change amount caused by generation of connection between fragment B and structure a of atomic assembly A in the change represented by reaction formula (1).
- ⁇ ( ⁇ ) in the third term in numerical formula (1) represents a free energy change amount in the change represented by reaction formula (1) when the interaction energy between structure a and fragment B connected to the structure a is ⁇ , and represents a free energy change amount caused by an interaction between fragment B and a part or the whole of an atomic assembly generated by removing structure aB consisting of structure a and fragment B connected to the structure a from atomic assembly AB.
- the third term ⁇ ( ⁇ )P( ⁇ )d ⁇ in numerical formula (1) represents a free energy change amount caused by interaction energy ⁇ in the change represented by reaction formula (1), and can be calculated by applying a conventional energy representation method using numerical formula (6) below. Notation on the left side in numerical formula (6) represents a distribution function like notation in the conventional energy representation method.
- fragment B contains a virtual atom(s) such as a point charge(s) described below
- atomic assembly AB is anisole (C 6 H 5 OCH 3 ) and fragment B is formed of a methoxy group (—OCH 3 ) and a point charge (virtual atom having a charge parameter contained in the benzene ring carbon atom to which the methoxy group is connected)
- removing fragment B from atomic assembly AB means removing the methoxy group and a charge parameter contained in the point charge from the anisole.
- atomic assembly A is an atomic assembly represented by C 6 H 5
- an atomic assembly in which the charge parameter contained in a benzene ring carbon atom to which the methoxy group is connected in atomic assembly AB is zero.
- fragment B is formed of a methoxy group (—OCH 3 ) and a point charge (virtual atom having a charge parameter contained in the benzene ring carbon atom to which the methoxy group is connected
- atomic assembly A is an atomic assembly in which a partial charge contained in the benzene ring carbon atom to which the methoxy group in fragment B is connected is zero
- connection of fragment B to atomic assembly A means forming a covalent bond between an oxygen atom of the methoxy group in fragment B and the benzene ring carbon atom, and adding a partial charge (charge parameter) contained in the point charge of fragment B to the charge parameter of a benzene ring carbon atom to which the oxygen atom
- a charge parameter contained in an atom may be referred to as a partial charge.
- removing a charge parameter(s) contained in a point charge(s) of fragment B from a charge parameter(s) of an atom(s) constituting atomic assembly AB may be referred to as removing the point charge(s) of fragment B from atomic assembly AB.
- adding a charge parameter(s) contained in a point charge(s) of fragment B to a charge parameter(s) of an atom(s) constituting atomic assembly AB may be referred to as adding the point charge(s) of fragment B to atomic assembly AB or adding the point charge(s) of fragment B to the charge parameter(s) of an atom(s) constituting atomic assembly AB.
- ⁇ ( ⁇ )P( ⁇ )d ⁇ in the third term in numerical formula (1) can be calculated without calculating ⁇ ( ⁇ ) based on P( ⁇ ) which is an appearance probability in each class of interaction energy ⁇ in atomic assembly AB after the change, P 0 ′( ⁇ ; ⁇ ) which is an appearance probability in each class of interaction energy ⁇ in each class of interaction energy ⁇ in atomic assembly AB generated by connection of fragment B to atomic assembly A before the change, and P′( ⁇ ) which is an appearance probability in each class of interaction energy ⁇ in atomic assembly AB after the change.
- ⁇ ( ⁇ )P( ⁇ )d ⁇ can be calculated by calculating a free energy change amount ⁇ ( ⁇ ) caused by interaction energy ⁇ in each class of interaction energy ⁇ , and using the calculated ⁇ ( ⁇ ) and P( ⁇ ) that is an appearance probability in each class of interaction energy ⁇ in atomic assembly AB after the change.
- ⁇ ⁇ ⁇ ( ⁇ ) ⁇ i ⁇ ⁇ ⁇ ( ⁇ - ( v ⁇ ( ⁇ , K , x i ) - u ⁇ ( K , x i ) ) ( 6 )
- a sampling efficiency can be improved significantly by adding an atom(s) constituting fragment B to an atom(s) constituting atomic assembly A. Therefore, a method of calculating ⁇ ( ⁇ ) is not particularly limited, but, for example, the conventional particle insertion method or energy representation method can be used. Note that a difference ⁇ G in free energy in numerical formula (1) can be applied to calculation of any difference in free energy such as a difference in solvation free energy or a difference in binding free energy.
- ⁇ G is a free energy change amount in change represented by reaction formula (1): A+B ⁇ AB (1)
- A represents an atomic assembly consisting of structure a or containing structure a
- B represents a fragment consisting of one or more atoms
- AB represents an atomic assembly consisting of atomic assembly A and fragment B connected to structure a of the atomic assembly A
- Each of atomic assembly A and atomic assembly AB is atomic assembly constituted by one or more atoms.
- Each of atomic assembly A and atomic assembly AB may contain one or more atoms not connected to another atom.
- the atom(s) includes an ion(s).
- the atom(s) includes a virtual atom(s) (nonexistent atom(s)).
- Examples of an interatomic connection constituting each of atomic assembly A and atomic assembly AB include a covalent bond, a coordination bond, a hydrogen bond, an electrostatic interaction, and a hydrophobic interaction.
- Each of atomic assembly A and atomic assembly AB may be constituted by one kind of interatomic connection (for example, a covalent bond) or a combination of two or more kinds of interatomic connections (for example, a combination of a covalent bond and one or more kinds of other interatomic connections).
- Each of atomic assembly A and atomic assembly AB may be constituted by one or more kinds of molecules.
- the molecule examples include a ligand(s), a protein(s) to which the ligand(s) is bound, and a solvent molecule(s) such as a water molecule(s).
- a ligand(s) When atomic assembly A is constituted by one kind of molecule, atomic assembly AB is also constituted by one kind of molecule.
- atomic assembly AB When atomic assembly A is constituted of two or more kinds of molecules, atomic assembly AB is also constituted by two or more kinds of molecules.
- Examples of when each of atomic assembly A and atomic assembly AB is constituted by two or more kinds of molecules include when each of atomic assembly A and atomic assembly AB contains a ligand(s), and further contains a protein(s) to which the ligand(s) is bound and/or a solvent molecule(s) such as a water molecule(s).
- a solvent molecule(s) such as a water molecule(s).
- the ligand(s) and the protein(s) may form a complex.
- Examples of a bond type(s) between a ligand and a protein in the complex include a coordination bond, a hydrogen bond, an electrostatic interaction, a covalent bond, and a hydrophobic interaction.
- examples of a bond type(s) between the ligand(s) or the complex(es) and a solvent molecule(s) such as a water molecule(s) include a coordination bond, a hydrogen bond, an electrostatic interaction, a covalent bond, and a hydrophobic interaction.
- Atomic assembly A is formed of structure a or contains structure a.
- structure a may be the whole of the structure of the molecule (in this case, atomic assembly A is formed of structure a), or may be a part of the structure of the molecule (in this case, atomic assembly A contains structure a).
- structure a may be the whole of the structure of the two or more molecules (in this case, atomic assembly A is formed of structure a), or may be a part of the structure of the two or more molecules (in this case, atomic assembly A contains structure a).
- atomic assembly A contains a complex(es) formed of a protein(s) and a ligand(s)
- examples of a part of the structure of the complex(es) include the whole or a part of the structure of the ligand(s), the whole or a part of the structure of the protein(s), a portion formed of the whole or a part of the ligand(s) and a part of the protein(s), and a portion formed of the whole or a part of a receptor(s) and a part of the ligand(s).
- Atomic assembly A corresponds to an atomic assembly obtained by removing fragment B from atomic assembly AB.
- atomic assembly AB is anisole (C 6 H 5 OCH 3 ) and fragment B is a methoxy group (—OCH 3 )
- atomic assembly A is C 6 H 5 .
- atomic assembly AB is anisole (C 6 H 5 OCH 3 ) and fragment B is formed of a methoxy group (—OCH 3 ) and a point charge (virtual atom having a charge parameter contained in a benzene ring carbon atom to which the methoxy group is connected)
- atomic assembly A is obtained by removing the methoxy group and the point charge from the anisole. That is, atomic assembly A is an atomic assembly represented by C 6 H 5 , and an atomic assembly in which the charge parameter contained in the benzene ring carbon atom to which the methoxy group was connected in atomic assembly AB is zero.
- Atomic assembly AB is formed of atomic assembly A and fragment B connected to structure a of the atomic assembly A.
- Atomic assembly AB corresponds to an atomic assembly in which fragment B is connected to atomic assembly A.
- atomic assembly A has a structure obtained by removing a methoxy group and a point charge (partial charge contained in the benzene ring carbon atom to which the methoxy group is connected) from anisole, and fragment B is formed of a methoxy group and the point charge
- atomic assembly AB is anisole.
- the number of atoms constituting structure a is not particularly limited as long as being one or more, but is preferably three or more, and more preferably five or more. When the number of atoms constituting structure a is three or more, connection of fragment B to structure a of atomic assembly A can be performed efficiently. Therefore, a sampling efficiency can be improved. In addition, an upper limit value of the number of atoms constituting structure a is not particularly limited.
- the kind of an atom constituting structure a is not particularly limited.
- Examples of an atom constituting structure a include a carbon atom, a hydrogen atom, a nitrogen atom, and an oxygen atom.
- Structure a may be constituted of one kind of atom or two or more kinds of atoms.
- a bond type(s) between atoms constituting structure a is not particularly limited.
- Examples of the bond type(s) between atoms constituting structure a include a covalent bond, a coordination bond, a hydrogen bond, an electrostatic interaction, and a hydrophobic interaction.
- Structure a may be constituted of one kind of interatomic connection (for example, a covalent bond) or a combination of two or more kinds of connections (for example, a combination of a covalent bond and one or more kinds of other connections).
- An atom constituting structure a may contain one or more virtual atoms (nonexistent atoms). Structure a may be constituted only by an existent atom(s), only by a virtual atom(s), or by a combination of an existent atom(s) and a virtual atom(s).
- Examples of the virtual atom include an atom in which a valence shell does not contain eight electrons formally. It is known that an atom corresponding to a typical element belonging to groups 1, 2, and 13 to 18 in the periodic table usually satisfies the octet rule by taking an electron arrangement formally having eight electrons in a valence shell thereof and exists in a chemically stable state.
- Examples of another virtual atom include a point charge not having an interaction for a bond involving a bond length, a bond angle, a twist angle or the like or a van der Waals interaction with another atom(s) (that is, having a van der Waals potential of zero) but having an electrostatic interaction(s) with another atom(s) (that is, having a charge parameter and a Coulomb potential), an atom having no electrostatic interactions with another atom(s) (that is, having a Coulomb potential of zero) but having an interaction(s) for a bond caused by a bond length, a bond angle, a twist angle or the like and a van der Waals interaction with another atom(s), an atom existing in an ionic state, and a dummy atom not having any of an interaction(s) for a bond caused by a bond length, a bond angle, a twist angle or the like, a van der Waals interaction, and an electrostatic interaction with another atom(s).
- the number of atoms constituting fragment B is not particularly limited as long as being one or more.
- An upper limit value of the number of atoms constituting fragment B is not particularly limited, but is usually 25, and preferably 10.
- the kind of an atom(s) constituting fragment B is not particularly limited.
- Examples of an atom(s) constituting fragment B include a carbon atom, a hydrogen atom, a nitrogen atom, and an oxygen atom.
- Fragment B may be constituted of one kind of atom or two or more kinds of atoms.
- a bond type(s) between atoms constituting fragment B is not particularly limited.
- Examples of the bond type(s) between atoms constituting fragment B include a covalent bond, a coordination bond, a hydrogen bond, an electrostatic interaction, and a hydrophobic interaction.
- Fragment B may be constituted of one kind of interatomic bond (for example, a covalent bond) or a combination of two or more kinds of bonds (for example, a combination of a covalent bond and one or more kinds of other bonds).
- An atom constituting fragment B may contain one or more virtual atoms (nonexistent atoms). Fragment B may be constituted only of an existent atom(s), only a virtual atom(s), or a combination of an existent atom(s) and a virtual atom(s). Examples of the virtual atom(s) include similar specific examples to structure a.
- fragment B contains a point charge(s) as a virtual atom(s) and is constituted a combination of an existent atom(s) and a virtual atom(s), there is no covalent bond(s) between the existent atom(s) and the virtual atom(s), and there are no interactions for the bond caused by the bond length, the bond angle, the twist angle, or the like between the existent atom(s) and the virtual atom(s).
- an electrostatic interaction between a virtual atom(s) (point charge) and an existent atom(s) in fragment B is preferably calculated. However, it does not matter whether the electrostatic interaction is calculated or not as long as being unified in a process of calculating free energy.
- aB is anisole (C 6 H 5 OCH 3 ) and fragment B is formed of a methoxy group (—OCH 3 ) and a point charge (virtual atom having a charge parameter contained in the benzene ring carbon atom to which the methoxy group is connected), it is preferable to calculate the electrostatic interaction between the point charge and each of the hydrogen atoms of the methoxy group.
- a calculation device 1 includes an input unit 11 , a control unit 12 , a storage unit 13 , and an output unit 14 connected to one another through a system bus.
- the calculation device 1 can be implemented by using a general-purpose computer as basic hardware.
- the input unit 11 is constituted of a pointing device such as a keyboard or a mouse operated by an operator, and inputs various operation signals such as an instruction by an operator (for example, an instruction to execute a program or an instruction to display a result of processing) or input of data required for processing.
- the control unit 12 causes the storage unit 13 to store the input data.
- the control unit 12 is constituted of CPU, RAM, ROM or the like, and calculates ⁇ G based on various data stored in the storage unit 13 , various programs or the like.
- the control unit 12 functions as a first atomic assembly model creation unit 12 A, a first coordinates acquisition unit 12 B, a second coordinates acquisition unit 12 C, a first interaction energy ⁇ frequency distribution creation unit 12 D, a first interaction energy ⁇ appearance probability calculation unit 12 E, a first interaction energy ⁇ frequency distribution creation unit 12 F, a first interaction energy appearance probability calculation unit 12 G, a second atomic assembly model creation unit 12 H, a third coordinates acquisition unit 12 I, a second interaction energy ⁇ frequency distribution creation unit 12 J, a second interaction energy ⁇ appearance probability calculation unit 12 K, a second interaction energy ⁇ frequency distribution creation unit 12 L, a second interaction energy ⁇ appearance probability calculation unit 12 M, a ⁇ ( ⁇ )P( ⁇ )d ⁇ calculation unit 12 N, and a
- CPU of the control unit 12 may include a plurality of arithmetic cores, and each of the arithmetic cores may function as various unit by execution of a calculation program to calculate ⁇ G. According to such a configuration, a plurality of calculations can be processed in parallel, and time required to calculate ⁇ G can be thereby reduced.
- the storage unit 13 is constituted of a storage such as RAM or a hard disc, and stores various data, various programs and the like.
- Examples of the data and program stored in the storage unit 13 include data 13 A for atomic assembly A before the change, data 13 B for a first simulation condition, a first simulation program 13 C, data 13 D for atomic assembly AB after the change, data 13 E for a second simulation condition, and a second simulation program 13 F.
- the first simulation program 13 C and the second simulation program 13 F are described as separate programs, but the first simulation program 13 C and the second simulation program 13 F may be one program.
- the output unit 14 is constituted of a display or the like, and outputs a result acquired or calculated by various units (for example, ⁇ G calculated by the ⁇ G calculation unit 12 O).
- the first atomic assembly model creation unit 12 A creates a first atomic assembly model modeling atomic assembly A before the change.
- the control unit 12 causes the storage unit 13 to store data for the first atomic assembly model created by the first atomic assembly model creation unit 12 A (for example, coordinates of each of atoms constituting atomic assembly A, the kind thereof, a mass thereof, a partial charge thereof, and interatomic bond information).
- the first atomic assembly model creation unit 12 A uses the data 13 A for atomic assembly A before the change that is stored in the storage unit 13 .
- the data 13 A for atomic assembly A before the change is stored in the storage unit 13 in a form of a file which can read by the control unit 12 .
- the data 13 A for atomic assembly A before the change is not particularly limited as long as the first atomic assembly model modeling atomic assembly A before the change can be created. Examples of the data 13 A for atomic assembly A before the change include coordinates of each of atoms constituting atomic assembly A, the kind thereof, a mass thereof, a partial charge thereof, and interatomic bond information.
- the first atomic assembly model is not particularly limited as long as computer simulation is possible.
- Examples of the atomic assembly model include an all-atom model, a beads spring model, and a united atom model.
- the beads spring model is a model in which a monomer unit constituting atomic assembly A is assumed to be one bead (segment) and the beads are connected with a virtual spring(s)
- the united atom model is a model in which a hydrogen atom is included in a heavy atom (for example, a carbon atom) and is handled as one atom (mass point).
- the first coordinates acquisition unit 12 B acquires coordinates of atomic assembly A in each of first to i th states F 1 to F i (wherein i is an integer of two or more) by a snapshot output as a result of computer simulation with respect to the first atomic assembly model created by the first atomic assembly model creation unit 12 A.
- the snapshot includes coordinates of all the atoms constituting atomic assembly A. That is, the snapshot in each of states F 1 to F i includes coordinates of all the atoms constituting atomic assembly A in each of states F 1 to F i .
- the control unit 12 causes the storage unit 13 to store coordinates of all the atoms constituting atomic assembly A, acquired by the first coordinates acquisition unit 12 B.
- Computer simulation performed by the first coordinates acquisition unit 12 B is not particularly limited as long as being based on a statistical mechanics theory.
- Examples of representative computer simulation include a molecular dynamics method, a Monte Carlo method, and a method obtained by combining the molecular dynamics method or the Monte Carlo method and a first-principle calculation.
- the first coordinates acquisition unit 12 B performs computer simulation based on the data for the first atomic assembly model, the data 13 B for the first simulation condition, the first simulation program 13 C and the like that are stored in the storage unit 13 .
- the data 13 B for the first simulation condition is stored in the storage unit 13 in a form of a file that can read by the control unit 12 .
- the simulation condition is not particularly limited as long as computer simulation can be performed.
- Examples of the simulation condition include a temperature condition, a pressure condition, the kind of a potential parameter(s) and a value(s) thereof, the kind of an ensemble to be generated, a boundary condition, and an output condition such as the number of snapshots.
- Examples of the potential parameter(s) include a parameter(s) for an interatomic bond(s) involving a bond length, a bond angle, a twist angle or the like, a van der Waals interaction that acts between atoms, and an electrostatic interaction.
- potential parameters examples include the known potential parameters such as Amber, GAFF, CHARMm (registered trademark), CGenFF (CHARMm36), DISCOVER, GROMOS, DREIDING, or OPLS.
- a parameter value(s) for a bond length, a bond angle, van der Waals or the like is determined based on an atom type assigned to each of the atoms constituting atomic assembly A and a combination of the atom types of the atoms.
- the potential parameters can be grouped into potential parameters for atomic bonds and non-bonding potential parameters not involved in presence or absence of a bond. When calculation accuracy is considered, it is preferable to determine the potential parameters by a method described below.
- HF method Hartree Fock method
- B3LYP method a density functional theory using B3LYP as a functional
- 6-31G(d) basis function, 6-31G(d,p) basis function, and 6-31+G(d,p) basis function can be used preferably.
- the non-bonding potential parameters can be further grouped into parameters for van der Waals potentials and parameters for Coulomb potentials.
- the former are preferably determined to reproduce experimental values of a density and vaporization heat.
- Each of the latter parameters is the partial charge belonging to an atom, and they are preferably determined to reproduce electrostatic potentials (ESP) determined from quantum chemical calculation.
- ESP electrostatic potentials
- a method for reproducing ESP a known MK method or CHelpG method can be used preferably.
- quantum chemical calculation program packages available for a fee or free of charge can be used.
- a general-purpose program commercially available or published under a product name such as “Gaussian98 (registered trademark)”, “Gaussian03 (registered trademark)”, “Gaussian09 (registered trademark)”, or “GAMESS” can be used preferably.
- first-principle calculation may be performed with respect to all the atoms constituting atomic assembly A, or first-principle calculation may be performed with respect to a part of the atoms constituting atomic assembly A and a molecular force field method may be performed with respect to the remaining atoms constituting atomic assembly A.
- the former case does not require bond information for each atom, a potential parameter(s), or an atom type(s). In the latter case, it is only necessary to adjust bond information, a potential parameter(s), an atom type or the like for each atom appropriately according to an atomic range to which first-principle calculation is applied.
- Examples of an ensemble to be generated by computer simulation include an NVE ensemble (the particle number N, volume V, and energy E are constant), an NVT ensemble (the particle number N, volume V, and temperature T are constant), and an NPT ensemble (the particle number N, pressure P, and volume V are constant). Note that the ensemble is a set of microscopic states that can be taken by a system (statistical set).
- Examples of a boundary condition include a periodic boundary condition.
- the periodic boundary condition is applied to molecular dynamics simulation, an image cell is arranged around a basic cell.
- a temperature condition is set to a temperature at which the change represented by reaction formula (1) occurs.
- the temperature is an absolute temperature represented by a unit of Kelvin (K).
- the first coordinates acquisition unit 12 B acquires coordinates of atomic assembly A in each of states F 1 to F i contained in an ensemble generated by computer simulation.
- states F 1 to F i is a microscopic state generated by performing computer simulation.
- States F 1 to F i may be a part or the whole of the microscopic state generated by computer simulation.
- a value of i is not particularly limited as long as being two or more, and can be selected appropriately according to the kind of free energy as a calculation target (for example, solvation free energy or binding free energy).
- a value of i is preferably 10000 or more, more preferably 100000 or more, and still more preferably 1000000 or more.
- a value of i is preferably 100000 or more, and more preferably 1000000 or more.
- An upper limit value of i is not particularly limited, but is usually 10000000, and preferably 5000000.
- a state of atomic assembly A changes over time from an initial state (time T 0 ) to state F 1 (time T 1 ), state F 2 (time T 2 ), . . . , and state F i (time T i ).
- Coordinates of atomic assembly A in each of states F 1 to F i are acquired along time series.
- Acquired coordinates of atomic assembly A in each of states F 1 to F i (time T 1 to T i ) (each time) are associated with each state (each time) in which the coordinates were acquired, and are caused to be stored in the storage unit 13 by the control unit 12 .
- states F 1 to F i are created by generating random numbers, and coordinates of atomic assembly A in each of states F 1 to F i are acquired. Acquired coordinates of atomic assembly A in each of states F 1 to F i are associated with each state in which the coordinates were acquired, and are caused to be stored in the storage unit 13 by the control unit 12 .
- the first coordinates acquisition unit 12 B preferably performs energy minimization calculation before performing molecular dynamics simulation with respect to the first atomic assembly model.
- the energy minimization calculation can be performed based on a function of the first simulation program 13 C stored in the storage unit 13 .
- the energy minimization calculation distortion of an unnatural structure contained in an initial structure of an atomic assembly model can be removed, and it is possible to avoid divergence of time integral in an initial stage of computer simulation.
- the first coordinates acquisition unit 12 B preferably equilibrates the first atomic assembly model (preferably an atomic assembly model after energy minimization calculation) to acquire coordinates of atomic assembly A in states F 1 to F i after the equilibration.
- the first coordinates acquisition unit 12 B performs computer simulation with respect to the first atomic assembly model (preferably, an atomic assembly model after energy minimization calculation). For example, when a fluctuation width of a certain physical quantity value reaches a constant value or when a certain time passes, the first coordinates acquisition unit 12 B determines that the atomic assembly model has been equilibrated and acquires coordinates of atomic assembly A in states F 1 to F i after the equilibration.
- the second coordinates acquisition unit 12 C acquires coordinates of atomic assembly AB generated by connection of fragment B to atomic assembly A in each of states F 1 to F i based on the coordinates of atomic assembly A acquired by the first coordinates acquisition unit 12 B.
- Coordinates of atomic assembly AB acquired by the second coordinates acquisition unit 12 C contain coordinates of all the atoms constituting atomic assembly AB.
- Acquired coordinates of atomic assembly AB are associated with a state of atomic assembly A as a base thereof, and are caused to be stored in the storage unit 13 by the control unit 12 . That is, coordinates R AB (F 1 ), R A (F 2 ), . . .
- R AB (F i ) of atomic assembly AB are associated with states F 1 , F 2 , . . . , and F i , respectively, and are caused to be stored in the storage unit 13 by the control unit 12 .
- Atomic assembly AB generated by connection of fragment B to atomic assembly A in state F x may be one kind of atomic assembly or two or more kinds of atomic assemblies. That is, coordinates R AB (F x ) may mean coordinates of atomic assembly AB generated by connection of each of the first, second, . . . , and p th fragments B having different relative positions with respect to structure a to atomic assembly A in state F x .
- the first, second, . . . , and p th fragments B may be noted by “fragment B 1 ”, “fragment B 2 ”, . . . , and “fragment B p ”, respectively.
- Coordinates of atomic assembly AB generated by connection of the fragments B 1 , B 2 , . . . , and B p to atomic assembly A in state F x may be noted by “R AB (F x ,B 1 )”, “R AB (F x ,B 2 )”, . . . , and “R AB (F x ,B p )”, respectively.
- Coordinates of atomic assembly AB generated by connection of the fragments B to atomic assembly A in state F x may be acquired by generating atomic assembly AB actually or without generating atomic assembly AB actually. In the latter case, for example, a relative position of fragment B to be connected to atomic assembly A in state F x with respect to structure a is determined, and coordinates R AB (F x ) of atomic assembly AB generated by connection of fragment B to atomic assembly A in state F x can be acquired based on coordinates of atomic assembly A in state F x and the determined relative position of fragment B with respect to structure a.
- a relative position of fragment B to be connected to atomic assembly A in state F x with respect to structure a is not particularly limited.
- the constraint condition is not particularly limited as long as being able to limit coordinates of an atom(s) constituting fragment B with respect to coordinates of an atom(s) constituting structure a.
- the constraint condition may be a condition to limit coordinates of a part of atoms constituting fragment B with respect to coordinates of an atom(s) constituting structure a, or a condition to limit coordinates of all the atoms constituting fragment B with respect to coordinates of an atom(s) constituting structure a.
- processing W 103 to acquire coordinates R Ab (F x ) of atomic assembly Ab generated by connection of atom b to atomic assembly A in state F x based on the acquired coordinates of atom b and coordinates R A (F x ) of atomic assembly A in state F x ;
- processing W 104 to generate coordinates of an atom(s) other than atom b, constituting fragment B by computer simulation, a known conformation generation method, or the like based on the coordinates of atom b, and to acquire coordinates R AB (F x ) of atomic assembly AB generated by connection of fragment B to atomic assembly A in state F x .
- Coordinates R AB (F 1 ) to R AB (F i ) of atomic assembly AB generated by connection of fragment B having a limited relative position with respect to structure a can be thereby acquired for atomic assembly A in each of states F 1 to F i .
- the second coordinates acquisition unit 12 C may define the first, second, . . . , and p th relative position conditions which are different from one another for fragment B to be connected to atomic assembly A in state F x .
- the second coordinates acquisition unit 12 C performs processing W 102 to W 104 repeatedly for each of the first to p th relative position conditions.
- Coordinates R AB (F x ,B 1 ), R AB (F x ,B 2 ), . . . , and R AB (F x ,B p ) of atomic assembly AB generated by connection of the fragments B 1 , B 2 , . . . , and B p having different relative positions with respect to structure a can be thereby acquired for atomic assembly A in state F x .
- the second coordinates acquisition unit 12 C performs the following processing:
- processing W 201 to create a third atomic assembly model modeling atomic assembly C consisting of structure a and fragment B connected to the structure a or containing structure a and fragment B connected to the structure a;
- coordinates of atomic assembly C in states H 1 , H 2 , . . . , and H k may be noted by “R C (H 1 )”, “R C (H 2 )”, . . . , and “R C (H k )”, respectively) in each of first to k th states H 1 to H k (wherein k is an integer of two or more) by computer simulation with respect to the created third atomic assembly model, and then
- processing W 203 to select a selected atomic group consisting of one or more atoms selected from atoms constituting structure a (note that not only when two or more atoms are selected but also when one atom is selected is referred to as a “selected atomic group” for convenience), to rotate and/or translate coordinates of a selected atomic group of atomic assembly C in one or more states selected from states H 1 to H k with respect to coordinates of a selected atomic group of atomic assembly A in state F x , thereby to create coordinates of atomic assembly C having the minimum sum of squares of distances between corresponding atoms between the selected atomic group of atomic assembly A and the selected atomic group of atomic assembly C (to fit coordinates of the selected atomic group of atomic assembly C to coordinates of the selected atomic group of atomic assembly A), and to superimpose atomic assembly C in one or more states selected from states H 1 to H k on atomic assembly A based on the created coordinates of atomic assembly C; and
- processing W 204 to acquire coordinates of atomic assembly AB generated by connection of fragment B to atomic assembly A in state F x based on coordinates R A (F x ) of atomic assembly A in state F x and one or more coordinates of fragment B in atomic assembly C superimposed on atomic assembly A in state F x .
- Coordinates R AB (F 1 ) to R AB (F i ) of atomic assembly AB generated by connection of fragment B having the limited relative position with respect to structure a can be thereby acquired for atomic assembly A in each of states F 1 to F i .
- Atomic assembly C may be constituted only of a molecule C′ consisting of structure a and fragment B connected to the structure a (in this case, surrounding of the molecule C′ is in vacuum), or by the molecule C′ consisting of structure a and fragment B connected to the structure a and one or more kinds of other molecules (for example, a solvent molecule(s) such as a water molecule(s)).
- a solvent molecule(s) such as a water molecule(s)
- the second coordinates acquisition unit 12 C creates a third atomic assembly model modeling atomic assembly C.
- the control unit 12 causes the storage unit 13 to store data for the third atomic assembly model created by the second coordinates acquisition unit 12 C (for example, coordinates of each of atoms constituting atomic assembly C, the kind thereof, a mass thereof, a partial charge thereof, and interatomic bond information).
- the second coordinates acquisition unit 12 C uses data (not illustrated) for atomic assembly C that is stored in the storage unit 13 .
- the data for atomic assembly C is stored in the storage unit 13 in a form of a file that can read by the control unit 12 .
- the data for atomic assembly C is not particularly limited as long as the third atomic assembly model modeling atomic assembly C can be created.
- Examples of the data for atomic assembly C include data for the molecule C′ (for example, coordinates of each of atoms constituting the molecule C′, the kind thereof, a mass thereof, a partial charge thereof, and interatomic bond information) and data for a surrounding environment of the molecule C′ (for example, presence or absence of a solvent molecule positioned around the molecule C′, the kind thereof, the number thereof, and coordinates of an atom constituting a solvent molecule).
- the third atomic assembly model is not particularly limited as long as computer simulation is possible.
- Examples of the atomic assembly model include an all-atom model, a beads spring model, and a united atom model.
- Computer simulation with respect to the third atomic assembly model is not particularly limited as long as being based on a statistical mechanics theory. Examples of representative computer simulation include a molecular dynamics method, a Monte Carlo method, and a method obtained by combining the molecular dynamics method or the Monte Carlo method and first-principle calculation. Computer simulation with respect to the third atomic assembly model can be performed in a similar manner to computer simulation with respect to the first atomic assembly model.
- the second coordinates acquisition unit 12 C preferably performs energy minimization calculation before performing molecular dynamics simulation with respect to the third atomic assembly model.
- the energy minimization calculation can be performed based on a function of the first simulation program 13 C stored in the storage unit 13 .
- the energy minimization calculation distortion of an unnatural structure contained in an initial structure of an atomic assembly model is removed, and it is possible to avoid divergence of time integral in an initial stage of computer simulation.
- the second coordinates acquisition unit 12 C preferably equilibrates the third atomic assembly model (preferably an atomic assembly model after energy minimization calculation) to acquire coordinates of atomic assembly C in states H 1 to H k after the equilibration.
- the second coordinates acquisition unit 12 C performs computer simulation with respect to the third atomic assembly model (preferably, an atomic assembly model after energy minimization calculation). For example, when a fluctuation width of a certain physical quantity value reaches a constant value or when a certain time passes, the second coordinates acquisition unit 12 C determines that the atomic assembly model has been equilibrated and acquires coordinates of atomic assembly C in states H 1 to H k after the equilibration.
- the second coordinates acquisition unit 12 C may select p sets of coordinates having different relative positions of fragment B with respect to structure a from coordinates of atomic assembly C in states H 1 to H k with respect to coordinates R A (F x ) of atomic assembly A in state F x .
- the second coordinates acquisition unit 12 C performs processing W 203 to W 204 repeatedly for each of the p sets of coordinates.
- Coordinates R AB (F x ,B 1 ), R AB (F x ,B 2 ), . . . , and R AB (F x ,B p ) of atomic assembly AB generated by connection of the fragments B 1 , B 2 , . . . , and B p having different relative positions with respect to structure a can be thereby acquired for atomic assembly A in state F x .
- processing W 203 as a method to rotate and/or translate coordinates of atomic assembly C in one or more states selected from states H 1 to H k with respect to coordinates R A (F x ) of atomic assembly A in state F x based on coordinates of a selected atomic group, and thereby to superimpose atomic assembly C in one or more states selected from states H 1 to H k on atomic assembly A, a least squares method is preferable.
- a specific method of performing the least squares method is not particularly limited.
- the least squares method can be performed as follows.
- coordinates of a selected atomic group among coordinates of atomic assembly A in states F 1 to F i are noted by “(x s_A:n , y s_A:n , z s_A:n )”
- coordinates of a selected atomic group among coordinates of atomic assembly C in one state selected from states H 1 to H k are noted by “(x C:n , y C:n , z C:n )”
- by rotating and/or translating coordinates of the selected atomic group of atomic assembly C under a condition to maintain relative coordinates (internal coordinates) between atoms in the selected atomic group among coordinates of atomic assembly C are determined to minimize numerical formula (7).
- n given as a subscript of coordinates is given to each of atoms constituting a selected atomic group, and each of coordinates (x s_A:n , y s_A:n , z s_A:n ) and (x T:n , y T:n , z T:n ) represent coordinates of each of atoms constituting a selected atomic group.
- Cn in numerical formula (7) can be set for each of atoms constituting a selected atomic group in atomic assembly A and atomic assembly C, and is a real number of zero or more.
- the second coordinates acquisition unit 12 C preferably adds the point charge(s) of fragment B to a charge parameter(s) of an atom(s) constituting structure a of atomic assembly A.
- the second coordinates acquisition unit 12 C preferably adds the point charge(s) of fragment B to a charge parameter(s) of an atom(s) constituting structure a of atomic assembly A.
- an atom(s) constituting fragment B except for a virtual atom(s) constitutes an electron withdrawing group or an electron donating group and where an atom(s) constituting structure a of atomistic assembly A is connected to the atom constituting fragment B
- a bond is generated between the atom constituting structure a of atomic assembly A and the atom constituting fragment B except for the virtual atom(s)
- usually, among the atoms constituting structure a of atomic assembly A, a partial charge (charge parameter) of an atom connected to fragment B and/or an atom(s) around the atom connected to fragment B changes.
- a method in which an atom(s) constituting structure a, having a partial charge(s) (charge parameter(s)) changed depending on presence or absence of a bond with fragment B is handled as an atom(s) (existent atom(s)) constituting fragment B, and is not handled as an atom(s) constituting structure a is considered.
- a point charge(s) having an equal charge(s) to the change amount of the partial charge(s) (charge parameter(s)) of the atom(s) as an atom(s) (virtual atom(s)) constituting fragment B a change between atomic assembly AB (final state) and atomic assembly A (initial state) can be reduced. Therefore, calculation accuracy can be improved.
- the first interaction energy ⁇ frequency distribution creation unit 12 D calculates interaction energy ⁇ between structure a and fragment B connected to the structure a based on the coordinates of atomic assembly AB acquired by the second coordinates acquisition unit 12 C, and creates a frequency distribution indicating a frequency in each class of interaction energy ⁇ .
- the control unit 12 causes the storage unit 13 to store the calculated interaction energy ⁇ and the created frequency distribution.
- Each class of interaction energy ⁇ is associated with coordinates of atomic assembly AB as a base of calculation thereof, and is caused to be stored in the storage unit 13 by the control unit 12 .
- Interaction energy ⁇ is calculated for each of coordinates R AB (F 1 ) to R AB (F i ) of atomic assembly AB.
- interaction energy ⁇ can be calculated based on a function of the first simulation program 13 C stored in the storage unit 13 .
- a simulation program and a potential parameter(s) used are not particularly limited.
- coordinates of atomic assembly AB are determined by computer simulation performed by the first coordinates acquisition unit 12 B. Therefore, it is preferable to use the same simulation program and potential parameter(s) as those used in computer simulation performed by the first coordinates acquisition unit 12 B.
- a frequency distribution indicating a frequency in each class of interaction energy ⁇ can be created as a histogram in which the horizontal axis indicates each class of interaction energy ⁇ and the vertical axis indicates a frequency in each class of interaction energy ⁇ .
- each class of interaction energy ⁇ can be created with interaction energy ⁇ positioned in the center while an interaction energy section [ ⁇ /2 to ⁇ + ⁇ /2] with an interaction energy interval ⁇ is used as a class interval.
- ⁇ in each interaction energy section may be constant in all the sections, or may be changed appropriately according to an interaction energy section.
- a P 0 ( ⁇ ) class interval ⁇ is preferably the same as a P( ⁇ ) class interval ⁇ , and the P( ⁇ ) class interval ⁇ is preferably caused to be the same as the P 0 ( ⁇ ) class interval ⁇ .
- the number of division of interaction energy ⁇ that is, the number of the class interval ⁇ is not particularly limited, but is preferably from 50 to 500, and more preferably from 250 to 500.
- the second term in numerical formula (1) includes a calculation process of dividing an appearance probability P( ⁇ ) of interaction energy ⁇ by an appearance probability P 0 ( ⁇ ) of interaction energy ⁇ . Therefore, when there is an interaction energy section in which P( ⁇ ) is not zero and P 0 ( ⁇ ) is zero, the second term in numerical formula (1) diverges, and free energy calculation based on numerical formula (1) is not possible. Therefore, in all the interaction energy sections [ ⁇ /2 to ⁇ + ⁇ /2], it is preferable to set ⁇ for each interaction energy section appropriately such that P 0 ( ⁇ ) is constant. By setting ⁇ for each interaction energy section appropriately and causing the P( ⁇ ) class interval ⁇ to be the same as the P 0 ( ⁇ ) class interval ⁇ , a calculation result can be obtained with a statistically high accuracy.
- the first interaction energy ⁇ appearance probability calculation unit 12 E calculates an appearance probability P 0 ( ⁇ ) in each class of interaction energy ⁇ based on the frequency distribution created by the first interaction energy ⁇ frequency distribution creation unit 12 D.
- the control unit 12 causes the storage unit 13 to store the calculated P 0 ( ⁇ ).
- the first interaction energy ⁇ appearance probability calculation unit 12 E can calculate an appearance probability P 0 ( ⁇ ) in each class of interaction energy ⁇ .
- normalization means dividing a frequency in each class of interaction energy ⁇ in a frequency distribution by the sum of frequencies in classes of interaction energy ⁇ .
- the first interaction energy ⁇ frequency distribution creation unit 12 F calculates interaction energy ⁇ between a part or the whole of an atomic assembly generated by removing structure aB consisting of structure a and fragment B connected to the structure a from atomic assembly AB, and fragment B based on the coordinates of atomic assembly AB acquired by the second coordinates acquisition unit 12 C, and creates a frequency distribution indicating a frequency in each class of interaction energy ⁇ in each class of interaction energy ⁇ in the frequency distribution created by the first interaction energy ⁇ frequency distribution creation unit 12 D.
- the control unit 12 causes the storage unit 13 to store the calculated interaction energy ⁇ and the created frequency distribution.
- the first interaction energy ⁇ frequency distribution creation unit 12 F calculates interaction energy ⁇ between a part or the whole of an atomic assembly generated by removing structure aB consisting of structure a and fragment B connected to the structure a from atomic assembly AB, and fragment B for each of coordinates R AB (F 1 ) to R AB (F i ) of atomic assembly AB based on the coordinates of atomic assembly AB acquired by the second coordinates acquisition unit 12 C, then extracts interaction energy ⁇ between a part or the whole of an atomic assembly generated by removing structure aB consisting of structure a and fragment B connected to the structure a from atomic assembly AB, and fragment B in each class of interaction energy ⁇ based on the frequency distribution created by the first interaction energy ⁇ frequency distribution creation unit 12 D, and creates a frequency distribution indicating a frequency in each class of interaction energy ⁇ in each class of interaction energy ⁇ in the frequency distribution created by the first interaction energy ⁇ frequency distribution creation unit 12 D.
- the first interaction energy ⁇ frequency distribution creation unit 12 F extracts coordinates of atomic assembly AB belonging to each class of interaction energy ⁇ from the coordinates of atomic assembly AB acquired by the second coordinates acquisition unit 12 C based on the frequency distribution created by the first interaction energy ⁇ frequency distribution creation unit 12 D, then calculates interaction energy ⁇ between a part or the whole of an atomic assembly generated by removing structure aB consisting of structure a and fragment B connected to the structure a from atomic assembly AB, and fragment B in each class of interaction energy ⁇ based on the extracted coordinates of atomic assembly AB, and creates a frequency distribution indicating a frequency in each class of interaction energy ⁇ in each class of interaction energy ⁇ in the frequency distribution created by the first interaction energy ⁇ frequency distribution creation unit 12 D.
- atomic assembly AB is constituted of a ligand(s) and a solvent molecule(s) (for example, a water molecule(s)), and structure aB consisting of structure a and fragment B connected to the structure a is the ligand(s), interaction energy ⁇ between a part or the whole of an atomic assembly generated by removing structure aB consisting of structure a and fragment B connected to the structure a from atomic assembly AB, and fragment B means an interaction energy between fragment B and each water molecule present around fragment B.
- interaction energy ⁇ between a part or the whole of an atomic assembly generated by removing structure aB consisting of structure a and fragment B connected to the structure a from atomic assembly AB, and fragment B means an interaction energy between fragment B and each water molecule, and an interaction energy between fragment B and the protein(s).
- Specific examples of interaction energy ⁇ , exemplified here are applied not only to interaction energy ⁇ calculated by the first interaction energy ⁇ frequency distribution creation unit 12 F but also to interaction energy ⁇ calculated by the second interaction energy ⁇ frequency distribution creation unit 12 L.
- Interaction energy ⁇ is calculated for all the classes of interaction energy ⁇ included in the frequency distribution (for example, histogram) created by the first interaction energy ⁇ frequency distribution creation unit 12 D.
- interaction energy ⁇ can be calculated based on a function of the first simulation program 13 C stored in the storage unit 13 .
- a simulation program and a potential parameter(s) used are not particularly limited.
- coordinates of atomic assembly AB are determined by computer simulation performed by the first coordinates acquisition unit 12 B. Therefore, it is preferable to use the same simulation program and potential parameter(s) as those used in computer simulation performed by the first coordinates acquisition unit 12 B.
- the frequency distribution indicating a frequency in each class of interaction energy ⁇ is created for interaction energy ⁇ in each class of interaction energy ⁇ .
- a frequency distribution indicating a frequency in each class of interaction energy ⁇ can be created as a histogram in which the horizontal axis indicates each class of interaction energy ⁇ and the vertical axis indicates a frequency in each class of interaction energy ⁇ .
- each class of interaction energy ⁇ can be created with interaction energy ⁇ positioned in the center while an interaction energy section [ ⁇ /2 to ⁇ + ⁇ /2] with an interaction energy interval ⁇ is used as a class interval.
- ⁇ in each interaction energy section may be constant in all the sections, or may be changed appropriately according to an interaction energy section.
- the number of division of interaction energy ⁇ that is, the number of the class intervals ⁇ is not particularly limited because of depending on the number of snapshots obtained by simulation, the number of water molecules or the like around fragment B, an energy section width of interaction energy ⁇ or the like. However, the number is preferably 500 to 5000, and more preferably 2000 to 5000.
- the first interaction energy ⁇ appearance probability calculation unit 12 G calculates an appearance probability P 0 ′( ⁇ ; ⁇ ) in each class of interaction energy ⁇ in each class of interaction energy ⁇ based on a frequency distribution created by the first interaction energy ⁇ frequency distribution creation unit 12 F.
- the control unit 12 causes the storage unit 13 to store the calculated P 0 ′( ⁇ ; ⁇ ). Note that “ ⁇ ” in P 0 ′( ⁇ ; ⁇ ) is a notation to clarify that an appearance probability P 0 ′( ⁇ ; ⁇ ) in each class of interaction energy ⁇ is calculated for each class of interaction energy ⁇ .
- the first interaction energy ⁇ appearance probability calculation unit 12 G can calculate an appearance probability P 0 ′( ⁇ ; ⁇ ) in each class of interaction energy ⁇ .
- normalization means dividing a frequency in each class of interaction energy ⁇ in a frequency distribution by the sum of frequencies in classes of interaction energy ⁇ .
- the second atomic assembly model creation unit 12 H creates a second atomic assembly model modeling atomic assembly AB after the change.
- the control unit 12 causes the storage unit 13 to store data for the second atomic assembly model created by the second atomic assembly model creation unit 12 H (for example, coordinates of each of atoms constituting atomic assembly AB, the kind thereof, a mass thereof, a partial charge thereof, and interatomic bond information).
- the second atomic assembly model creation unit 12 H uses the data 13 D for atomic assembly AB after the change that is stored in the storage unit 13 .
- the data 13 D for atomic assembly AB after the change is stored in the storage unit 13 in a form of a file that can read by the control unit 12 .
- the data 13 D for atomic assembly AB after the change is not particularly limited as long as the second atomic assembly model modeling atomic assembly AB after the change can be created.
- Examples of the data 13 D for atomic assembly AB after the change include coordinates of each of atoms constituting atomic assembly AB, the kind thereof, a mass thereof, a partial charge thereof, and interatomic bond information.
- the second atomic assembly model is not particularly limited as long as computer simulation is possible.
- the atomic assembly model include an all-atom model, a beads spring model, and a united atom model.
- the beads spring model is a model in which a monomer unit constituting atomic assembly AB is assumed to be one bead (segment) and the beads are connected with a virtual spring(s), and that the united atom model is a model in which a hydrogen atom is included in a heavy atom (for example, a carbon atom) and is handled as one atom (mass point).
- the third coordinates acquisition unit 12 I acquires coordinates of atomic assembly AB in each of first to j th states G 1 to G j (wherein j is an integer of two or more) by a snapshot output as a result of computer simulation with respect to the second atomic assembly model created by the second atomic assembly model creation unit 12 H.
- the snapshot includes coordinates of all the atoms constituting atomic assembly AB. That is, the snapshot in each of states G 1 to G j includes coordinates of all the atoms constituting atomic assembly AB in each of states G 1 to G j .
- G j may be referred to as coordinates R AB (G 1 ), R AB (G 2 ), . . . , and R AB (G j ), respectively.
- the control unit 12 causes the storage unit 13 to store the coordinates of atomic assembly AB, acquired by the third coordinates acquisition unit.
- Computer simulation performed by the third coordinates acquisition unit 12 I is not particularly limited as long as being based on a statistical mechanics theory.
- Examples of representative computer simulation include a molecular dynamics method, a Monte Carlo method, and a method obtained by combining the molecular dynamics method or the Monte Carlo method and first-principle calculation.
- the third coordinates acquisition unit 12 I performs computer simulation based on data for the second atomic assembly model, the data 13 E for the second simulation condition, the second simulation program 13 F and the like that stored in the storage unit 13 .
- the data 13 E for the simulation condition is stored in the storage unit 13 in a form of a file that can read by the control unit 12 .
- the simulation condition is not particularly limited as long as computer simulation can be performed. Specific description of computer simulation is similar to that of computer simulation performed by the first coordinates acquisition unit 12 B, and will be omitted.
- the third coordinates acquisition unit 12 I acquires coordinates of atomic assembly AB in each of states G 1 to G j contained in an ensemble generated by computer simulation.
- states G 1 to G j is a microscopic state generated by performing computer simulation.
- States G 1 to G j may be a part or the whole of the microscopic state generated by computer simulation.
- a value of j is not particularly limited as long as being two or more, and can be selected appropriately according to the kind of free energy as a calculation target (for example, solvation free energy or binding free energy).
- a value of j is preferably 10000 or more, and more preferably 100000 or more.
- a value of j is preferably 100000 or more, and more preferably 1000000 or more.
- An upper limit value of j is not particularly limited, but is usually 10000000, and preferably 5000000.
- a state of atomic assembly AB changes over time from an initial state (time T 0 ) to state G 1 (time T 1 ), state G 2 (time T 2 ), . . . , and state G j (time T j ).
- Coordinates of atomic assembly AB in each of states G 1 to G j are acquired along time series.
- Acquired coordinates of atomic assembly AB in each of states G 1 to G j (time T 1 to T j ) (each time) are associated with each state (each time) in which the coordinates were acquired, and are caused to be stored in the storage unit 13 by the control unit 12 .
- states G 1 to G j are created by generating random numbers, and coordinates of atomic assembly AB in each of states G 1 to G j are acquired. Acquired coordinates of atomic assembly AB in each of states G 1 to G j are associated with each state in which the coordinates were acquired, and are caused to be stored in the storage unit 13 by the control unit 12 .
- the third coordinates acquisition unit 12 I preferably performs energy minimization calculation before performing molecular dynamics simulation with respect to the second atomic assembly model.
- the energy minimization calculation can be performed based on a function of the second simulation program 13 F stored in the storage unit 13 .
- the energy minimization calculation distortion of an unnatural structure contained in an initial structure of an atomic assembly model is removed, and it is possible to avoid divergence of time integral in an initial stage of computer simulation.
- the third coordinates acquisition unit 12 I preferably equilibrates the second atomic assembly model (preferably, an atomic assembly model after energy minimization calculation) to acquire coordinates of atomic assembly AB in states G 1 to G j after the equilibration.
- the third coordinates acquisition unit 12 I performs computer simulation with respect to the second atomic assembly model (preferably, an atomic assembly model after energy minimization calculation). For example, when a certain physical quantity reaches a threshold value or when a certain time passes, the third coordinates acquisition unit 12 I determines that the atomic assembly model has been equilibrated and acquires coordinates of atomic assembly AB in states G 1 to G j after the equilibration.
- the second interaction energy ⁇ frequency distribution creation unit 12 J calculates interaction energy ⁇ between structure a and fragment B connected to the structure a based on the coordinates of atomic assembly AB acquired by the third coordinates acquisition unit 12 I, and creates a frequency distribution indicating a frequency in each class of interaction energy ⁇ .
- Each class of interaction energy ⁇ is associated with coordinates of atomic assembly AB as a base of calculation thereof, and is caused to be stored in the storage unit 13 by the control unit 12 .
- Interaction energy ⁇ is calculated for each of coordinates R AB (G 1 ) to R AB (G j ) of atomic assembly AB.
- interaction energy ⁇ can be calculated based on a function of the second simulation program 13 F.
- a simulation program and a potential parameter(s) used are not particularly limited.
- coordinates of atomic assembly AB are determined by computer simulation performed by the third coordinates acquisition unit 12 I. Therefore, it is preferable to use the same simulation program and potential parameter(s) as those used in computer simulation performed by the third coordinates acquisition unit 12 I.
- a frequency distribution indicating a frequency in each class of interaction energy ⁇ can be created as a histogram in which the horizontal axis indicates each class of interaction energy ⁇ and the vertical axis indicates a frequency in each class of interaction energy ⁇ .
- each class of interaction energy ⁇ can be created with interaction energy ⁇ positioned in the center while an interaction energy section [ ⁇ /2 to ⁇ + ⁇ /2] with an interaction energy interval ⁇ is used as a class interval.
- ⁇ in each interaction energy section may be constant in all the sections, or may be changed appropriately according to an interaction energy section.
- a P 0 ( ⁇ ) class interval ⁇ is preferably the same as a P( ⁇ ) class interval ⁇ , and the P( ⁇ ) class interval ⁇ is more preferably caused to be the same as the P 0 ( ⁇ ) class interval ⁇ .
- the number of division of interaction energy ⁇ that is, the number of the class interval ⁇ is not particularly limited, but is preferably 50 to 500, and more preferably 250 to 500.
- the second term in numerical formula (1) includes a calculation process for dividing an interaction energy appearance probability P( ⁇ ) by an interaction energy appearance probability P 0 ( ⁇ ). Therefore, when there is an interaction energy section in which P( ⁇ ) is not zero and the interaction energy appearance probability P 0 ( ⁇ ) is zero, the second term in numerical formula (1) diverges, and free energy calculation based on numerical formula (1) is not possible. Therefore, in all the interaction energy sections [ ⁇ /2 to ⁇ + ⁇ /2], it is preferable to set ⁇ for each interaction energy section appropriately such that P 0 ( ⁇ ) is constant. By setting ⁇ for each interaction energy section appropriately and causing the P( ⁇ ) class interval ⁇ to be the same as the P 0 ( ⁇ ) class interval ⁇ , a calculation result can be obtained with a statistically high accuracy.
- the second interaction energy ⁇ appearance probability calculation unit 12 K calculates an appearance probability P( ⁇ ) in each class of interaction energy ⁇ based on a frequency distribution created by the second interaction energy ⁇ frequency distribution creation unit 12 J.
- the control unit 12 causes the storage unit 13 to store the calculated P( ⁇ ).
- the second interaction energy ⁇ appearance probability calculation unit 12 K can calculate an appearance probability P( ⁇ ) in each class of interaction energy ⁇ .
- normalization means dividing a frequency in each class of interaction energy ⁇ in a frequency distribution by the sum of frequencies in classes of interaction energy ⁇ .
- the second interaction energy ⁇ frequency distribution creation unit 12 L calculates interaction energy ⁇ between a part or the whole of an atomic assembly generated by removing structure aB consisting of structure a and fragment B connected to the structure a from atomic assembly AB, and fragment B based on the coordinates of atomic assembly AB acquired by the third coordinates acquisition unit 12 I, and creates a frequency distribution indicating a frequency in each class of interaction energy ⁇ .
- the control unit 12 causes the storage unit 13 to store the calculated interaction energy ⁇ and the created frequency distribution.
- the second interaction energy ⁇ frequency distribution creation unit 12 L may calculate interaction energy ⁇ with or without associating interaction energy ⁇ with each class of interaction energy ⁇ in the frequency distribution created by the second interaction energy ⁇ frequency distribution creation unit 12 J.
- interaction energy ⁇ is calculated by being associated with each class of interaction energy ⁇
- interaction energy ⁇ is calculated for all the classes of interaction energy ⁇ included in the frequency distribution (for example, histogram) created by the second interaction energy ⁇ frequency distribution creation unit 12 J, and the frequency distribution indicating a frequency in each class of interaction energy ⁇ is created for interaction energy ⁇ in each class of interaction energy ⁇ .
- the second interaction energy ⁇ frequency distribution creation unit 12 L calculates interaction energy ⁇ between a part or the whole of an atomic assembly generated by removing structure aB consisting of structure a and fragment B connected to the structure a from atomic assembly AB, and fragment B for each of the coordinates R AB (G 1 ) to R AB (G j ) of atomic assembly AB, based on the coordinates of atomic assembly AB acquired by the third coordinates acquisition unit 12 I, and creates a frequency distribution indicating a frequency in each class of interaction energy ⁇ .
- the second interaction energy ⁇ frequency distribution creation unit 12 L calculates interaction energy ⁇ between a part or the whole of an atomic assembly generated by removing structure aB consisting of structure a and fragment B connected to the structure a from atomic assembly AB, and fragment B based on the coordinates of atomic assembly AB acquired by the third coordinates acquisition unit 12 I, and creates a frequency distribution indicating a frequency in each class of interaction energy ⁇ in each class of interaction energy ⁇ in the frequency distribution created by the second interaction energy ⁇ frequency distribution creation unit 12 J.
- the second interaction energy ⁇ frequency distribution creation unit 12 L calculates interaction energy ⁇ between a part or the whole of an atomic assembly generated by removing structure aB consisting of structure a and fragment B connected to the structure a from atomic assembly AB, and fragment B based on the coordinates of atomic assembly AB acquired by the third coordinates acquisition unit 12 I for each of coordinates R AB (G 1 ) to R AB (G j ) of atomic assembly AB, then extracts interaction energy ⁇ between a part or the whole of an atomic assembly generated by removing structure aB consisting of structure a and fragment B connected to the structure a from atomic assembly AB, and fragment B in each class of interaction energy ⁇ based on the frequency distribution created by the second interaction energy ⁇ frequency distribution creation unit 12 J, and creates a frequency distribution indicating a frequency in each class of interaction energy ⁇ in each class of interaction energy ⁇ in the frequency distribution created by the second interaction energy ⁇ frequency distribution creation unit 12 J.
- the second interaction energy ⁇ frequency distribution creation unit 12 L extracts coordinates of atomic assembly AB belonging to each class of interaction energy ⁇ from the coordinates of atomic assembly AB acquired by the third coordinates acquisition unit 12 I based on the frequency distribution created by the second interaction energy ⁇ frequency distribution creation unit 12 J, then calculates interaction energy ⁇ between a part or the whole of an atomic assembly generated by removing structure aB consisting of structure a and fragment B connected to the structure a from atomic assembly AB, and fragment B in each class of interaction energy ⁇ based on the extracted coordinates of atomic assembly AB, and creates a frequency distribution indicating a frequency in each class of interaction energy ⁇ in each class of interaction energy ⁇ in the frequency distribution created by the second interaction energy ⁇ frequency distribution creation unit 12 J.
- interaction energy ⁇ can be calculated based on a function of the second simulation program 13 F.
- a simulation program and a potential parameter used are not particularly limited.
- coordinates of atomic assembly AB are determined by computer simulation performed by the third coordinates acquisition unit 12 I. Therefore, it is preferable to use the same simulation program and potential parameter(s)r as those used in computer simulation performed by the third coordinates acquisition unit 12 I.
- a frequency distribution indicating a frequency in each class of interaction energy ⁇ can be created as a histogram in which the horizontal axis indicates each class of interaction energy ⁇ and the vertical axis indicates a frequency in each class of interaction energy ⁇ .
- each class of interaction energy ⁇ can be created with interaction energy ⁇ positioned in the center while an interaction energy section [ ⁇ /2 to ⁇ + ⁇ /2] with an interaction energy interval ⁇ is used as a class interval.
- ⁇ in each interaction energy section may be constant in all the sections, or may be changed appropriately according to an interaction energy section.
- a P 0 ′( ⁇ ; ⁇ ) class interval ⁇ is preferably the same as a P′( ⁇ ) class interval ⁇ .
- the number of division of interaction energy ⁇ that is, the number of the class intervals ⁇ is not particularly limited because of depending on the number of snapshots obtained by simulation, the number of water molecules around fragment B, an energy section width of interaction energy ⁇ or the like. However, the number is preferably 500 to 5000, and more preferably 2000 to 5000.
- the second interaction energy ⁇ appearance probability calculation unit 12 M calculates an appearance probability P′( ⁇ ) in each class of interaction energy ⁇ based on a frequency distribution created by the second interaction energy ⁇ frequency distribution creation unit 12 L.
- the control unit 12 causes the storage unit 13 to store the calculated P′( ⁇ ).
- the second interaction energy ⁇ appearance probability calculation unit 12 M can calculate an appearance probability P′( ⁇ ) in each class of interaction energy ⁇ .
- normalization means dividing a frequency in each class of interaction energy ⁇ in a frequency distribution by the sum of frequencies in classes of interaction energy ⁇ .
- the second interaction energy ⁇ frequency distribution creation unit 12 L calculates interaction energy ⁇ without associating interaction energy ⁇ with each class of interaction energy ⁇ in the frequency distribution created by the second interaction energy ⁇ frequency distribution creation unit 12 J
- the second interaction energy ⁇ appearance probability calculation unit 12 M calculates an appearance probability P′( ⁇ ) in each class of interaction energy ⁇ without associating the appearance probability P′( ⁇ ) with each class of interaction energy ⁇ based on the frequency distribution created by the second interaction energy ⁇ frequency distribution creation unit 12 L.
- the second interaction energy ⁇ frequency distribution creation unit 12 L calculates interaction energy ⁇ by associating interaction energy ⁇ with each class of interaction energy ⁇ in the frequency distribution created by the second interaction energy ⁇ frequency distribution creation unit 12 J
- the second interaction energy ⁇ appearance probability calculation unit 12 M calculates an appearance probability P′( ⁇ ; ⁇ ) in each class of interaction energy ⁇ in each class of interaction energy ⁇ based on the frequency distribution created by the second interaction energy ⁇ frequency distribution creation unit 12 L.
- ⁇ in P′( ⁇ ; ⁇ ) is a notation to clarify that an appearance probability P′( ⁇ ; ⁇ ) in each class of interaction energy ⁇ is calculated for each class of interaction energy ⁇ .
- the ⁇ ( ⁇ )P( ⁇ )d ⁇ calculation unit 12 N calculates a free energy change amount ⁇ ( ⁇ )P( ⁇ )d ⁇ caused by interaction energy ⁇ based on P( ⁇ ) calculated by the second interaction energy ⁇ appearance probability calculation unit 12 K, P 0 ′( ⁇ ; ⁇ ) calculated by the first interaction energy ⁇ appearance probability calculation unit 12 G, and P′( ⁇ ) calculated by the second interaction energy ⁇ appearance probability calculation unit 12 M.
- ⁇ ( ⁇ )” in “ ⁇ ( ⁇ )P( ⁇ )d ⁇ ” indicates a free energy change amount caused by interaction energy ⁇ in each class of interaction energy ⁇ .
- atomic assembly AB is constituted of a ligand(s) and a solvent molecule(s) (for example, a water molecule(s)), and structure aB consisting of structure a and fragment B connected to the structure a is the ligand(s)
- the free energy change amount caused by interaction energy ⁇ means a free energy change amount caused by an interaction energy between fragment B and a water molecule(s) present around fragment B.
- the free energy change amount caused by interaction energy ⁇ means the sum of a free energy change amount caused by an interaction energy between fragment B and the water molecule(s) and a free energy change amount caused by an interaction energy between fragment B and the protein(s).
- the ⁇ ( ⁇ )P( ⁇ )d ⁇ calculation unit 12 N preferably calculates a free energy change amount ⁇ ( ⁇ )P( ⁇ )d ⁇ caused by interaction energy ⁇ based on P( ⁇ ) calculated by the second interaction energy ⁇ appearance probability calculation unit 12 K, P 0 ′( ⁇ ; ⁇ ) calculated by the first interaction energy ⁇ appearance probability calculation unit 12 G, and P′( ⁇ ) calculated by the second interaction energy ⁇ appearance probability calculation unit 12 M by the energy representation method.
- the ⁇ ( ⁇ )P( ⁇ )d ⁇ calculation unit 12 N does not calculate ⁇ ( ⁇ ), but calculates ⁇ ( ⁇ )P( ⁇ )d ⁇ based on P( ⁇ ) calculated by the second interaction energy ⁇ appearance probability calculation unit 12 K, P 0 ′( ⁇ ; ⁇ ) calculated by the first interaction energy ⁇ appearance probability calculation unit 12 G, and P′( ⁇ ) calculated by the second interaction energy ⁇ appearance probability calculation unit 12 M by the energy representation method.
- P′( ⁇ ) used here is an appearance probability in each class of interaction energy ⁇ calculated without being associated with each class of interaction energy ⁇ .
- the ⁇ ( ⁇ )P( ⁇ )d ⁇ calculation unit 12 N calculates a free energy change amount ⁇ ( ⁇ ) caused by interaction energy ⁇ in each class of interaction energy ⁇ based on P 0 ′( ⁇ ; ⁇ ) calculated by the first interaction energy ⁇ appearance probability calculation unit 12 G and P′( ⁇ ; ⁇ ) calculated by the second interaction energy ⁇ appearance probability calculation unit 12 M, and calculates ⁇ ( ⁇ )P( ⁇ )d ⁇ based on the calculated ⁇ ( ⁇ ) and P( ⁇ ) calculated by the second interaction energy ⁇ appearance probability calculation unit 12 K.
- the ⁇ ( ⁇ )P( ⁇ )d ⁇ calculation unit 12 N preferably calculates a free energy change amount ⁇ ( ⁇ ) caused by interaction energy ⁇ in each class of interaction energy ⁇ based on P 0 ′( ⁇ ; ⁇ ) calculated by the first interaction energy ⁇ appearance probability calculation unit 12 G and P′( ⁇ ; ⁇ ) calculated by the second interaction energy ⁇ appearance probability calculation unit 12 M by the energy representation method.
- the ⁇ G calculation unit 12 O calculates ⁇ G based on P 0 ( ⁇ ) calculated by the first interaction energy ⁇ appearance probability calculation unit 12 E, P( ⁇ ) calculated by the second interaction energy ⁇ appearance probability calculation unit 12 K, ⁇ ( ⁇ )P( ⁇ )d ⁇ calculated by the ⁇ ( ⁇ )P( ⁇ )d ⁇ calculation unit 12 N, and numerical formula (1):
- ⁇ ⁇ ⁇ G ⁇ ⁇ ⁇ ⁇ P ⁇ ( ⁇ ) ⁇ d ⁇ ⁇ ⁇ + RT ⁇ ⁇ P ⁇ ( ⁇ ) ⁇ log ⁇ ( P ⁇ ( ⁇ ) P 0 ⁇ ( ⁇ ) ) ⁇ d ⁇ ⁇ ⁇ + ⁇ ⁇ ⁇ ⁇ v ⁇ ( ⁇ ) ⁇ P ⁇ ( ⁇ ) ⁇ d ⁇ ⁇ ⁇ ( 1 )
- R represents a gas constant
- T represents an absolute temperature at which the change represented by reaction formula (1) occurs.
- FIG. 2 is a flowchart illustrating a processing procedure of the calculation device 1 according to this example.
- control unit 12 When the control unit 12 performs calculation processing for atomic assembly A before the change (steps S 110 to 190 ) and calculation processing for atomic assembly AB after the change (steps S 210 to 280 ), the control unit 12 may perform one processing and then may perform the other processing, or may perform both the processing in parallel.
- steps S 110 to S 150 are described.
- the control unit 12 performs steps S 110 to S 150 sequentially.
- step S 110 the control unit 12 creates the first atomic assembly model modeling atomic assembly A before the change using the data 13 A for atomic assembly A before the change that is stored in the storage unit 13 .
- the control unit 12 causes the storage unit 13 to store the created data for the first atomic assembly model.
- the control unit 12 functions as the first atomic assembly model creation unit 12 A.
- step S 120 the control unit 12 acquires coordinates of atomic assembly A in each of first to i th states F 1 to F i (wherein i is an integer of two or more) by computer simulation with respect to the first atomic assembly model using data for the first atomic assembly model, the data 13 B for the first simulation condition, the first simulation program 13 C and the like that are stored in the storage unit 13 .
- the control unit 12 functions as the first coordinates acquisition unit 12 B.
- FIG. 3 illustrates an example of step S 120 performed by the control unit 12 when a molecular dynamics method is used as computer simulation.
- the control unit 12 performs energy minimization calculation with respect to the first atomic assembly model (step S 121 ), and subsequently equilibrates the first atomic assembly model (step S 122 ) to acquire coordinates of atomic assembly A in each of states F 1 to F i after the equilibration by computer simulation with respect to the first atomic assembly model after the equilibration.
- step S 122 for example, when a certain physical quantity in the first atomic assembly model reaches a threshold value or when a certain time passes after start of computer simulation, the control unit 12 determines that the first atomic assembly model has been equilibrated.
- step S 130 the control unit 12 acquires coordinates of atomic assembly AB generated by connection of fragment B to atomic assembly A in each of states F 1 to F i based on the coordinates of atomic assembly A acquired in step S 120 .
- the control unit 12 functions as the second coordinates acquisition unit 12 C.
- FIG. 4 illustrates an example of step S 130 performed by the control unit 12 .
- the control unit 12 performs the following steps after step S 120 :
- step S 131 a to define a relative position condition (for example, a distance(s) or an angle(s) with respect to one or more atoms constituting structure a) of atom b selected from atoms constituting fragment B with respect to structure a for fragment B to be connected to atomic assembly A in state F x ;
- step S 132 a to acquire coordinates of atom b based on the defined relative position condition
- step S 133 a to acquire coordinates R Ab (F x ) of atomic assembly Ab generated by connection of atom b to atomic assembly A in state F x based on the acquired coordinates of atom b and coordinates R A (F x ) of atomic assembly A in state F x ;
- step S 134 a to generate coordinates of an atom(s) other than atom b, constituting fragment B by computer simulation, known conformation generation methods, or the like based on coordinates of atom b, and to acquire coordinates R AB (F x ) of atomic assembly AB generated by connection of fragment B to atomic assembly A in state F x .
- Coordinates R AB (F 1 ) to R AB (F i ) of atomic assembly AB generated by connection of fragment B having a limited relative position with respect to structure a can be thereby acquired for atomic assembly A in each of states F 1 to F i .
- the control unit 12 may define the first, second, . . . , and p th relative position conditions which are different from one another for fragment B to be connected to atomic assembly A in state F x .
- step S 131 a when the first, second, . . . , and p th relative position conditions which are different from one another are defined for fragment B to be connected to atomic assembly A in state F x , the control unit 12 performs steps S 132 a to S 134 a repeatedly for each of the first to p th relative position conditions. Coordinates R AB (F x ,B 1 ), R AB (F x ,B 2 ), . . . , and R AB (F x ,B p ) of atomic assembly AB generated by connection of the fragments B 1 , B 2 , . . . , and B p having different relative positions with respect to structure a can be thereby acquired for atomic assembly A in state F x .
- FIG. 5 illustrates a preferable example of step S 130 performed by the control unit 12 .
- the control unit 12 performs the following steps:
- step S 131 b to create a third atomic assembly model modeling atomic assembly C consisting of structure a and fragment B connected to the structure a or containing structure a and fragment B connected to the structure a;
- step S 132 b to acquire coordinates of atomic assembly C in each of first to k th states H 1 to H k (wherein k is an integer of two or more) by computer simulation with respect to the created third atomic assembly model, and then
- step S 133 b to select a selected atomic group consisting of one or more atoms selected from atoms constituting structure a (note that not only a case where two or more atoms are selected but also a case where one atom is selected is referred to as a “selected atomic group” for convenience), to rotate and/or translate coordinates of a selected atomic group of atomic assembly C in one or more states selected from states H 1 to H k with respect to coordinates of a selected atomic group of atomic assembly A in state F x , thereby to create coordinates of atomic assembly C having the minimum sum of squares of distances between corresponding atoms between the selected atomic group of atomic assembly A and the selected atomic group of atomic assembly C (to fit coordinates of the selected atomic group of atomic assembly C to coordinates of the selected atomic group of atomic assembly A), and to superimpose atomic assembly C in one or more states selected from states H 1 to H k on atomic assembly A based on the created coordinates of atomic assembly
- step S 134 b to acquire coordinates of atomic assembly AB generated by connection of fragment B to atomic assembly A in state F x based on coordinates of atomic assembly A in state F x and one or more coordinates of fragment B in atomic assembly C superimposed on atomic assembly A.
- step S 135 b Coordinates R AB (F 1 ) to R AB (F i ) of atomic assembly AB generated by connection of fragment B having a limited relative position with respect to structure a can be thereby acquired for atomic assembly A in each of states F 1 to F i .
- step S 133 b the control unit 12 may select p sets of coordinates having different relative positions of fragment B to structure a from coordinates of atomic assembly C in states H 1 to H k .
- step S 133 b when p sets of coordinates having different relative positions of fragment B to structure a are selected from coordinates of atomic assembly C in states H 1 to H k , the control unit 12 performs steps S 133 b and S 134 b repeatedly for each of the p sets of coordinates.
- Coordinates R AB (F x ,B 1 ), R AB (F x ,B 2 ), . . . , and R AB (F x ,B p ) of atomic assembly AB generated by connection of the fragments B 1 , B 2 , . . . , and B p having different relative positions with respect to structure a can be thereby acquired for atomic assembly A in state F x .
- step S 140 the control unit 12 calculates interaction energy ⁇ between structure a and fragment B connected to the structure a based on the coordinates of atomic assembly AB acquired in step S 130 , and, in step S 150 , creates a frequency distribution indicating a frequency in each class of interaction energy ⁇ .
- step S 150 the control unit 12 functions as the first interaction energy ⁇ frequency distribution creation unit 12 D.
- steps S 160 to S 190 are described.
- step S 150 the control unit 12 performs processing for interaction energy ⁇ (step S 160 ) and processing for interaction energy ⁇ (steps S 170 to S 190 ).
- the control unit 12 may perform steps S 170 to S 190 after performing step S 160 , may perform step S 160 after performing steps S 170 to S 190 , or may perform step S 160 and steps S 170 to S 190 in parallel. In any case, the control unit 12 performs steps S 170 to S 190 sequentially.
- step S 160 the control unit 12 calculates an appearance probability P 0 ( ⁇ ) in each class of interaction energy ⁇ based on the frequency distribution created in step S 150 .
- step S 160 the control unit 12 functions as the first interaction energy ⁇ appearance probability calculation unit 12 E.
- step S 170 the control unit 12 calculates interaction energy ⁇ between a part or the whole of an atomic assembly generated by removing structure aB consisting of structure a and fragment B connected to the structure a from atomic assembly AB, and fragment B based on the coordinates of atomic assembly AB acquired in step S 130 .
- step S 180 the control unit 12 creates a frequency distribution indicating a frequency in each class of interaction energy ⁇ in each class of interaction energy ⁇ of the frequency distribution created in step S 150 .
- steps S 170 and S 180 the control unit 12 functions as the first interaction energy ⁇ frequency distribution creation unit 12 F.
- step S 170 the control unit 12 calculates interaction energy ⁇ between a part or the whole of an atomic assembly generated by removing structure aB consisting of structure a and fragment B connected to the structure a from atomic assembly AB, and fragment B for each of coordinates R AB (F 1 ) to R AB (F i ) of atomic assembly AB based on the coordinates of atomic assembly AB acquired in step S 130 , then extracts interaction energy ⁇ between a part or the whole of an atomic assembly generated by removing structure aB from atomic assembly AB and fragment B in each class of interaction energy ⁇ based on the coordinates of atomic assembly AB acquired in step S 130 and the frequency distribution created in step S 150 , and may create a frequency distribution indicating a frequency in each class of interaction energy ⁇ in each class of interaction energy ⁇ of the frequency distribution created in step S 150 .
- control unit 12 extracts coordinates of atomic assembly AB belonging to each class of interaction energy ⁇ from the coordinates of atomic assembly AB acquired in step S 130 based on the frequency distribution created in step S 150 , then calculates interaction energy ⁇ between a part or the whole of an atomic assembly generated by removing structure aB consisting of structure a and fragment B connected to the structure a from atomic assembly AB, and fragment B in each class of interaction energy ⁇ based on the extracted coordinates of atomic assembly AB, and may create a frequency distribution indicating a frequency in each class of interaction energy ⁇ in each class of interaction energy ⁇ in the frequency distribution created in step S 150 .
- step S 190 the control unit 12 calculates an appearance probability P 0 ′( ⁇ ; ⁇ ) in each class of interaction energy ⁇ in each class of interaction energy ⁇ based on the frequency distribution created in step S 180 .
- step S 190 the control unit 12 functions as the first interaction energy ⁇ appearance probability calculation unit 12 G.
- the control unit 12 performs steps S 210 to S 240 sequentially.
- step S 210 the control unit 12 creates the second atomic assembly model modeling atomic assembly AB after the change using the data 13 D for atomic assembly AB after the change that is stored in the storage unit 13 .
- the control unit 12 causes the storage unit 13 to store the created data for the second atomic assembly model.
- the control unit 12 functions as the second atomic assembly model creation unit 12 H.
- step S 220 the control unit 12 acquires coordinates of atomic assembly AB in each of first to j th states G 1 to G j (wherein j is an integer of two or more) by computer simulation with respect to the second atomic assembly model using the data for the second atomic assembly model, the data 13 E for the second simulation condition, the second simulation program 13 F and the like that are stored in the storage unit 13 .
- step S 220 the control unit 12 functions as the third coordinates acquisition unit 12 I.
- FIG. 6 illustrates an example of step S 220 performed by the control unit 12 when a molecular dynamics method is used as computer simulation.
- the control unit 12 performs energy minimization calculation with respect to the second atomic assembly model (step S 221 ), and subsequently equilibrates the second atomic assembly model (step S 222 ) to acquire coordinates of atomic assembly AB in each of states G 1 to G j after the equilibration by computer simulation with respect to the second atomic assembly model after the equilibration.
- step S 222 for example, when a certain physical quantity in the second atomic assembly model reaches a threshold value or when a certain time passes after start of computer simulation, the control unit 12 determines that the second atomic assembly model has been equilibrated.
- step S 230 the control unit 12 calculates interaction energy ⁇ between structure a and fragment B connected to the structure a based on the coordinates of atomic assembly AB acquired in step S 220 , and creates a frequency distribution indicating a frequency in each class of interaction energy ⁇ in step S 240 .
- the control unit 12 functions as the second interaction energy ⁇ frequency distribution creation unit 12 J.
- steps S 250 to S 280 are described.
- step S 240 the control unit 12 performs processing for interaction energy ⁇ (step S 250 ) and processing for interaction energy ⁇ (steps S 260 to S 280 ).
- the control unit 12 may perform steps S 260 to S 280 after performing step S 250 , may perform step S 250 after performing steps S 260 to S 280 , or may perform step S 250 and steps S 260 to S 280 in parallel. In any case, the control unit 12 performs steps S 260 to S 280 sequentially.
- step S 250 the control unit 12 calculates an appearance probability P( ⁇ ) in each class of interaction energy ⁇ based on the frequency distribution created in step S 240 .
- step S 250 the control unit 12 functions as the second interaction energy ⁇ appearance probability calculation unit 12 K.
- step S 260 the control unit 12 calculates interaction energy ⁇ between a part or the whole of an atomic assembly generated by removing structure aB consisting of structure a and fragment B connected to the structure a from atomic assembly AB, and fragment B based on the coordinates of atomic assembly AB acquired in step S 220 .
- step S 270 the control unit 12 creates a frequency distribution indicating a frequency in each class of interaction energy ⁇ .
- the control unit 12 functions as the second interaction energy ⁇ frequency distribution creation unit 12 L.
- the control unit 12 may calculate interaction energy ⁇ with or without associating interaction energy ⁇ with each class of interaction energy ⁇ in the frequency distribution created by step S 240 .
- interaction energy ⁇ is calculated by being associated with each class of interaction energy ⁇
- interaction energy ⁇ is calculated for all the classes of interaction energy ⁇ included in the frequency distribution (for example, histogram) created in step S 240 , and the frequency distribution indicating a frequency in each class of interaction energy ⁇ is created for interaction energy ⁇ in each class of interaction energy ⁇ .
- control unit 12 calculates interaction energy ⁇ without associating interaction energy ⁇ with each class of interaction energy ⁇
- the control unit 12 calculates interaction energy ⁇ between a part or the whole of an atomic assembly generated by removing structure aB consisting of structure a and fragment B connected to the structure a from atomic assembly AB, and fragment B based on the coordinates of atomic assembly AB acquired in step S 220 for each of coordinates R AB (G 1 ) to R AB (G j ) of atomic assembly AB, and creates a frequency distribution indicating a frequency in each class of interaction energy ⁇ .
- control unit 12 calculates interaction energy ⁇ by associating interaction energy ⁇ with each class of interaction energy ⁇
- the control unit 12 calculates interaction energy ⁇ between a part or the whole of an atomic assembly generated by removing structure aB consisting of structure a and fragment B connected to the structure a from atomic assembly AB, and fragment B based on the coordinates of atomic assembly AB acquired in step S 220 , and creates a frequency distribution indicating a frequency in each class of interaction energy ⁇ in each class of interaction energy ⁇ of the frequency distribution created in step S 240 .
- control unit 12 calculates interaction energy ⁇ between a part or the whole of an atomic assembly generated by removing structure aB consisting of structure a and fragment B connected to the structure a from atomic assembly AB, and fragment B for each of coordinates R AB (G 1 ) to R AB (G j ) of atomic assembly AB based on the coordinates of atomic assembly AB acquired in step S 220 , then extracts interaction energy ⁇ between a part or the whole of an atomic assembly generated by removing structure aB consisting of structure a and fragment B connected to the structure a from atomic assembly AB, and fragment B in each class of interaction energy ⁇ based on the frequency distribution created in step S 240 , and creates a frequency distribution indicating a frequency in each class of interaction energy ⁇ in each class of interaction energy ⁇ in the frequency distribution created in step S 240 .
- control unit 12 extracts coordinates of atomic assembly AB belonging to each class of interaction energy ⁇ from the coordinates of atomic assembly AB acquired in step S 220 based on the frequency distribution created in step S 240 , then calculates interaction energy ⁇ between a part or the whole of an atomic assembly generated by removing structure aB consisting of structure a and fragment B connected to the structure a from atomic assembly AB, and fragment B in each class of interaction energy ⁇ based on the extracted coordinates of atomic assembly AB, and creates a frequency distribution indicating a frequency in each class of interaction energy ⁇ in each class of interaction energy ⁇ in the frequency distribution created in step S 240 .
- control unit 12 calculates interaction energy ⁇ without associating interaction energy ⁇ with each class of interaction energy ⁇ , in steps S 260 and S 270 , the control unit 12 calculates interaction energy ⁇ between a part or the whole of an atomic assembly generated by removing structure aB consisting of structure a and fragment B connected to the structure a from atomic assembly AB, and fragment B based on the coordinates of atomic assembly AB acquired in step S 220 for each of coordinates R AB (G 1 ) to R AB (G j ) of atomic assembly AB, and creates a frequency distribution indicating a frequency in each class of interaction energy ⁇ .
- control unit 12 calculates interaction energy ⁇ by associating interaction energy ⁇ with each class of interaction energy ⁇ , in steps S 260 and S 270 , the control unit 12 calculates interaction energy ⁇ between a part or the whole of an atomic assembly generated by removing structure aB consisting of structure a and fragment B connected to the structure a from atomic assembly AB, and fragment B based on the coordinates of atomic assembly AB acquired in step S 220 for each of coordinates R AB (G 1 ) to R AB (G j ) of atomic assembly AB, then extracts interaction energy ⁇ between a part or the whole of an atomic assembly generated by removing structure aB from atomic assembly AB and fragment B in each class of interaction energy ⁇ based on the frequency distribution created in step S 240 , and may create a frequency distribution indicating a frequency in each class of interaction energy ⁇ in each class of interaction energy ⁇ of the frequency distribution created in step S 240 .
- control unit 12 extracts coordinates of atomic assembly AB belonging to each class of interaction energy ⁇ from the coordinates of atomic assembly AB acquired in step S 220 based on the frequency distribution created in step S 240 , then calculates interaction energy ⁇ between a part or the whole of an atomic assembly generated by removing structure aB from atomic assembly AB, and fragment B in each class of interaction energy ⁇ based on the extracted coordinates of atomic assembly AB, and may create a frequency distribution indicating a frequency in each class of interaction energy ⁇ in each class of interaction energy ⁇ in the frequency distribution created in step S 240 .
- step S 280 the control unit 12 calculates an appearance probability P′( ⁇ ) in each class of interaction energy ⁇ based on the frequency distribution created in step S 270 .
- step S 280 the control unit 12 functions as the second interaction energy ⁇ appearance probability calculation unit 12 M.
- steps S 260 and S 270 when the control unit 12 calculates interaction energy ⁇ without associating interaction energy ⁇ with each class of interaction energy ⁇ in the frequency distribution created in step S 240 , and creates a frequency distribution in each class of interaction energy ⁇ , in step S 280 , the control unit 12 calculates an appearance probability P′( ⁇ ) in each class of interaction energy ⁇ without associating the appearance probability P′( ⁇ ) with each class of interaction energy ⁇ based on the frequency distribution created in step S 270 .
- steps S 260 and S 270 when the control unit 12 calculates interaction energy ⁇ by associating interaction energy ⁇ with each class of interaction energy ⁇ in the frequency distribution created in step S 240 , and creates a frequency distribution in each class of interaction energy ⁇ , in step S 280 , the control unit 12 calculates an appearance probability P′( ⁇ ; ⁇ ) in each class of interaction energy ⁇ in each class of interaction energy ⁇ based on the frequency distribution created in step S 270 .
- step S 300 is described.
- the control unit 12 performs calculation processing for atomic assembly A before the change (steps S 110 to S 190 ) and calculation processing for atomic assembly AB after the change (steps S 210 to S 280 ), and then performs calculation processing for a free energy change amount ⁇ ( ⁇ )P( ⁇ )d ⁇ (step S 300 ).
- step S 300 the control unit 12 calculates a free energy change amount ⁇ ( ⁇ )P( ⁇ )d ⁇ caused by interaction energy ⁇ based on P( ⁇ ) calculated in step S 250 , P 0 ′( ⁇ ; ⁇ ) calculated in step S 190 , and P′( ⁇ ) calculated in step S 280 .
- the control unit 12 functions as the ⁇ ( ⁇ )P( ⁇ )d ⁇ calculation unit 12 N.
- control unit 12 does not calculate ⁇ ( ⁇ ), but calculates ⁇ ( ⁇ )P( ⁇ )d ⁇ based on P( ⁇ ) calculated in step S 250 , P 0 ′( ⁇ ; ⁇ ) calculated in step S 190 , and P′( ⁇ ) calculated in step S 280 by the energy representation method.
- P′( ⁇ ) used here is an appearance probability in each class of interaction energy ⁇ calculated without being associated with each class of interaction energy ⁇ .
- control unit 12 calculates a free energy change amount ⁇ ( ⁇ ) caused by interaction energy ⁇ in each class of interaction energy ⁇ based on P 0 ′( ⁇ ; ⁇ ) calculated in step S 190 and P′( ⁇ ; ⁇ ) calculated in step S 280 , and calculates ⁇ ( ⁇ )P( ⁇ )d ⁇ based on the calculated ⁇ ( ⁇ ) and P( ⁇ ) calculated in step S 250 .
- the ⁇ ( ⁇ )P( ⁇ )d ⁇ calculation unit 12 N preferably calculates a free energy change amount ⁇ ( ⁇ ) caused by interaction energy ⁇ in each class of interaction energy ⁇ based on P 0 ′( ⁇ ; ⁇ ) calculated in step S 190 and P′( ⁇ ; ⁇ ) calculated in step S 280 by the energy representation method.
- step S 400 is described.
- the control unit 12 performs calculation processing for a free energy change amount ⁇ ( ⁇ )P( ⁇ )d ⁇ (step S 300 ), and then performs calculation processing for ⁇ G (step S 400 ).
- step S 400 the control unit 12 calculates ⁇ G based on P 0 ( ⁇ ) calculated in step S 160 , P( ⁇ ) calculated in step S 250 , ⁇ ( ⁇ )P( ⁇ )d ⁇ calculated in step S 300 , and numerical formula (1):
- ⁇ ⁇ ⁇ G ⁇ ⁇ ⁇ ⁇ P ⁇ ( ⁇ ) ⁇ d ⁇ ⁇ ⁇ + RT ⁇ ⁇ P ⁇ ( ⁇ ) ⁇ log ⁇ ( P ⁇ ( ⁇ ) P 0 ⁇ ( ⁇ ) ) ⁇ d ⁇ ⁇ ⁇ + ⁇ ⁇ ⁇ ⁇ v ⁇ ( ⁇ ) ⁇ P ⁇ ( ⁇ ) ⁇ d ⁇ ⁇ ⁇ ( 1 )
- R represents a gas constant
- T represents an absolute temperature at which the change represented by reaction formula (1) occurs.
- a function of the calculation device 1 according to this example can be implemented by using a computer-readable recording medium with a program to cause the control unit 12 to function as the first atomic assembly model creation unit 12 A, the first coordinates acquisition unit 12 B, the second coordinates acquisition unit 12 C, the first interaction energy ⁇ frequency distribution creation unit 12 D, the first interaction energy ⁇ appearance probability calculation unit 12 E, the first interaction energy ⁇ frequency distribution creation unit 12 F, the first interaction energy ⁇ appearance probability calculation unit 12 G, the second atomic assembly model creation unit 12 H, the third coordinates acquisition unit 12 I, the second interaction energy ⁇ frequency distribution creation unit 12 J, the second interaction energy ⁇ appearance probability calculation unit 12 K, the second interaction energy ⁇ frequency distribution creation unit 12 L, the second interaction energy ⁇ appearance probability calculation unit 12 M, the ⁇ ( ⁇ )P( ⁇ )d ⁇ calculation unit 12 N, and the ⁇ G calculation unit 12 O (that is, a program to cause the control unit 12 to perform steps S 110 to S 190 , steps S 210 to S 280 , step S 300 ,
- Examples of the computer-readable recording medium with a program recorded thereon include ROM, a floppy disk (registered trademark), a hard disk, an optical disk, a magnetooptical disk, CD-ROM, a magnetic tape, and a nonvolatile memory card.
- This disclosure includes not only an example to implement a function of the calculation device 1 according to this example by execution of a program by a computer but also an example to implement a function of the calculation device 1 according to this example by association of a program with OS (operating system) running in a computer, another application software or the like.
- this disclosure also includes an example to implement a function of the calculation device 1 according to this example by execution of a part or the whole of actual processing by CPU or the like included in a function expansion board of a computer or a function expansion unit connected to the computer based on an instruction of a program after the program is stored in a memory provided in the function expansion board or the function expansion unit.
- R represents a protein
- ⁇ surrounding R represents presence of water molecules around protein R
- L 1 represents a ligand bound to protein R
- ⁇ surrounding L 1 represents presence of water molecules around ligand L 1
- L 1 R represents a complex formed of protein R and ligand L 1 bound to the protein R
- ⁇ surrounding L 1 R represents presence of water molecules around complex L 1 R
- L 2 represents a ligand bound to protein R, different from ligand L 1
- ⁇ surrounding L 2 represents presence of water molecules around ligand L 2
- L 2 R represents a complex formed of protein R and ligand L 2 bound to the protein R
- ⁇ surrounding L 2 R represents presence of water molecules around complex L 2 R.
- ⁇ G3 is a difference in free energy between ligand L 1 having water molecules therearound and ligand L 2 having water molecules therearound.
- both a fragment removed in a change of L 1 R ⁇ L 0 R and a fragment added in a change of L 0 R ⁇ L 2 R are represented by “B” for convenience, but the fragment removed in the change of L 1 R ⁇ L 0 R is actually different from the fragment added in the change of L 0 R ⁇ L 2 R. Details of the fragment removed in the change of L 1 R ⁇ L 0 R and the fragment added in the change of L 0 R ⁇ L 2 R are described below.
- L 0 R represents a complex formed of protein R and ligand L 0 bound to the protein R, and ⁇ surrounding L 0 R represents presence of water molecules around the complex L 0 R.
- both a fragment removed in a change of L 1 ⁇ L 0 and a fragment added in a change of L 0 ⁇ L 2 are represented by “B” for convenience, but the fragment removed in the change of L 1 ⁇ L 0 is actually different from the fragment added in the change of L 0 ⁇ L 2 . Details of the fragment removed in the change of L 1 ⁇ L 0 and the fragment added in the change of L 0 ⁇ L 2 are described below.
- L 0 represents a ligand bound to protein R, different from ligand L 1 or ligand L 2 , and ⁇ surrounding L 0 represents presence of water molecules around ligand L 0 .
- R does not interact with any one of L 1 , L 2 , and L 0 . Therefore, ⁇ G3 in reaction formula (6) means a difference in free energy between ligand L 1 having water molecules therearound and ligand L 2 having water molecules therearound.
- atomic assembly constituting complex L 0 R and water molecules present around the complex L 0 R before the change was referred to as “atomic assembly A”
- atomic assembly constituting complex L 1 R and water molecules present around the complex L 1 R after the change was referred to as “atomic assembly AB”
- a difference ⁇ G4a′ between the sum of free energy of atomic assembly A before the change and free energy of fragment B, and free energy of atomic assembly AB after the change was calculated based on numerical formula (1).
- ⁇ G4a is a free energy change amount regarding change represented by the following reaction formula (8).
- trypsin that is a kind of serine protease was selected.
- ligand L 1 As ligand L 1 , benzamidine that is a trypsin inhibitor was selected.
- a chemical structure of ligand L 1 is as follows.
- a partial charge of each of atoms constituting ligand L 1 is as follows. Four decimal places of the partial charge were rounded off to three decimal places. A partial charge described below is similar. Note that these partial charges were created by the MATCH program described below.
- ligand L 0 a molecule obtained by removing fragment B formed of a hydrogen atom connected to the benzene ring carbon atom at a para position of an amidine group and a point charge having a partial charge ( ⁇ 0.115) of the benzene ring carbon atom to which the hydrogen atom was connected from ligand L 1 was selected.
- a chemical structure of ligand L 0 is as follows.
- a partial charge of each of atoms constituting ligand L 0 is as follows.
- fragment B a hydrogen atom and a point charge (partial charge; ⁇ 0.115) were selected.
- the hydrogen atom is connected to the benzene ring in ligand L 1 , and the point charge has a partial charge ( ⁇ 0.115) contained in the carbon atom to which the hydrogen atom was connected in ligand L 1 .
- ligand L 0 a molecule in which the partial charge of the carbon atom to which the hydrogen atom of fragment B was connected among the carbon atoms constituting the benzene ring is zero was obtained as ligand L 0 .
- the structure of fragment B is as follows.
- the point charge having a partial charge ( ⁇ 0.115) is not connected to the hydrogen atom.
- ligand L 0 All the atoms constituting ligand L 0 were selected from the structures of ligands L 0 and L 1 , and were referred to as “structure a”. Therefore, ligand L 0 is formed of structure a, and ligand L 1 is formed of structure a and fragment B connected to the structure a.
- ⁇ G4a′ was calculated by performing steps S 110 A to S 190 A, S 210 A to S 280 A, S 300 A, and S 400 A corresponding to steps S 110 to S 190 , S 210 to S 280 , S 300 , and S 400 illustrated in FIG. 2 using the calculation device illustrated in FIG. 1 .
- steps S 121 A to S 123 A corresponding to steps S 121 to S 123 illustrated in FIG. 3 were performed.
- steps S 131 A to S 134 A corresponding to steps S 131 b to S 134 b illustrated in FIG. 5 were performed.
- steps S 221 A to S 223 A steps S 221 to S 223 illustrated in FIG. 6 were performed.
- the input unit 11 input data for complex L 0 R contained in atomic assembly A before the change and complex L 1 R contained in atomic assembly AB after the change (coordinates of each of atoms constituting complex L 1 R, the kind thereof, a mass thereof, a partial charge thereof, interatomic bond information or the like, and coordinates of each of atoms constituting complex L 0 R, the kind thereof, a mass thereof, a partial charge thereof, interatomic bond information or the like) in the control unit 12 .
- the kind of an atom means the kind of an element in the periodic table and an atomic type.
- An atomic type of each atom or a pair of atomic types between atoms is given to correspond to a value of a potential parameter at one to one.
- the control unit 12 caused the storage unit 13 to store the input data.
- Data for complex L 1 R contained in atomic assembly AB after the change was obtained by using a three-dimensional structure data file (3PTB_AB) created by removing oxygen atoms attributed to water molecules included in the three-dimensional structure data file (PDB code: 3PTB) downloaded from the three-dimensional structure database protein data bank (PDB) using the integrated computational chemistry system molecular operating environment (MOE) provided by Chemical Computing Group (CCG) Co., Ltd., and then adding hydrogen atoms and coordinates of the hydrogen atoms to the three-dimensional structure data file using the “protonate 3D” function mounted on MOE, and by using the “automatic PSF builder” function mounted on the visualization software visual molecular dynamics (VMD).
- 3PTB_AB three-dimensional structure data file created by removing oxygen atoms attributed to water molecules included in the three-dimensional structure data file
- PDB code: 3PTB three-dimensional structure database protein data bank
- MOE integrated computational chemistry system molecular operating environment
- CCG Chemical Computing Group
- the three-dimensional structure data (PDB code: 3PTB) included coordinates data for calcium, and the calcium was handled as an ion or a part of the protein.
- data for complex L 0 R contained in atomic assembly A before the change was created using the “automatic PSF builder” function of VMD based on the three-dimensional structure data file (3PTB_A) created by removing atoms other than the point charge as a virtual atom constituting fragment B from the three-dimensional structure data file (3PTB_AB) using the “builder” function of MOE.
- the three-dimensional structure data file (3PTB_AB) includes coordinates data for complex L 1 R.
- Data for ligand L 1 is selected from the three-dimensional structure data file (3PTB_AB) using MOE, a three-dimensional structure data file (3PTB_L 1 ) for ligand L 1 is created, and data for ligand L 1 can be obtained by the “automatic PSF builder” function of VMD.
- data for ligand L 0 was obtained by creating a three-dimensional structure data file (3PTB_L 0 ) for ligand L 0 from the three-dimensional structure data file (3PTB_A) and setting the partial charge of the benzene ring carbon atom connected to the atom (that is, a hydrogen atom) constituting fragment B except for the virtual atom to zero.
- the input unit 11 input simulation conditions for energy minimization calculation (the number of calculations of a force applied to each atom, the kind of a potential parameter(s) and a value(s) thereof, a boundary condition, a switching function and a cut-off radius for van der Waals potential and Coulomb potential calculation, a long-distance interaction in Coulomb potential calculation, a condition for a 1-4 interaction and the like) and simulation conditions for molecular dynamics simulation (simulation time, a temperature condition, a pressure condition, the kind of a potential parameter(s) and a value(s) thereof, the kind of an ensemble generated, a boundary condition, a numerical solution of an equation of motion, a time step of numerical integration, a switching function and a cut-off radius for van der Waals potential and Coulomb potential calculation, a condition for a long-distance interaction in Coulomb potential calculation, a 1-4 interaction, an output condition such as the number of snapshots and the
- CHARMm22 was used as the kind of a potential parameter of each of atoms constituting protein R.
- Charmm general forcefield (CGenFF) was used as the kind of a potential parameter(s) of each of atoms constituting ligand L 0 and the kind of a potential parameter(s) of each of atoms constituting ligand L 1 .
- TIP3P was used as the kind of a potential parameter(s) of each of atoms constituting water molecules. Note that a potential parameter(s) of each of atoms constituting ligand L 0 and a potential parameter(s) of each of atoms constituting ligand L 1 were determined using the MATCH program.
- Step S 110 A Creation of First Atomic Assembly Model
- step S 110 A the control unit 12 read the three-dimensional structure data file (3PTB_A) stored in the storage unit 13 using visualization software VMD, then created a rectangular type basic cell in which 9492 water molecules had been generated around complex L 0 R formed of protein R and ligand L 0 bound to the protein R using a “solvate” function mounted on the VMD, and created the first atomic assembly model modeling atomic assembly A before the change.
- the control unit 12 caused the storage unit 13 to store data for the created first atomic assembly model (coordinates of each of atoms constituting atomic assembly A, the kind thereof, a mass thereof, a partial charge thereof, interatomic bond information and the like).
- the kind of an atom means the kind of an element in the periodic table and an atomic type to designate a potential parameter(s) used in computer simulation.
- Step S 120 A Acquisition of Coordinates of Atomic Assembly A by Computer Simulation
- step S 120 A the control unit 12 performed the following steps S 121 A to S 123 A.
- Step S 121 A Energy Minimization Calculation with Respect to First Atomic Assembly Model
- step S 121 A with respect to the first atomic assembly model, the control unit 12 caused the molecular dynamics simulation program NAMD program to read simulation conditions for energy minimization calculation (the number of calculations of a force applied to each atom, the kind of a potential parameter(s) and a value(s) thereof, a boundary condition, a switching function and a cut-off radius for van der Waals potential and Coulomb potential calculation, a long-distance interaction in Coulomb potential calculation, a condition for a 1-4 interaction and the like), and performed energy minimization calculation using the “minimize” function of NAMD.
- energy minimization calculation the number of calculations of a force applied to each atom, the kind of a potential parameter(s) and a value(s) thereof, a boundary condition, a switching function and a cut-off radius for van der Waals potential and Coulomb potential calculation, a long-distance interaction in Coulomb potential calculation, a condition for a 1-4 interaction and the like
- the control unit 12 caused the storage unit 13 to store data for the first atomic assembly model after the energy minimization calculation (coordinates of each of atoms constituting atomic assembly A, the kind thereof, a mass thereof, a partial charge thereof, an atomic type thereof, interatomic bond information and the like).
- the kind of an atom means the kind of an element in the periodic table and an atomic type to designate a potential parameter(s) used in computer simulation.
- a condition of the energy minimization calculation is as follows.
- boundary condition a periodic boundary condition was employed.
- number of calculations in the input file of the NAMD program, “minimize” was set to 10000.
- a keyword “switching” for the switching function used for van der Waals potential and Coulomb potential calculation was set to 10 angstroms, and a keyword “cutoff” for the cut-off radius was set to 12 angstroms.
- PME particle mesh ewald
- Step S 122 A Equilibration of First Atomic Assembly Model
- step S 122 A the control unit 12 caused the NAMD program to read data for the first atomic assembly model after the energy minimization calculation that is stored in the storage unit 13 (coordinates of each of atoms constituting atomic assembly A, the kind thereof, a mass thereof, a partial charge thereof, interatomic bond information and the like) and data for a simulation condition (simulation time, a temperature condition, a pressure condition, the kind of a potential parameter(s) and a value(s) thereof, the kind of an ensemble generated, a boundary condition, a numerical solution of an equation of motion, a time step of numerical integration, a switching function and a cut-off radius for van der Waals potential and Coulomb potential calculation, a long-distance interaction in Coulomb potential calculation, a condition for a 1-4 interaction, an output condition such as the number of snapshots and the like), performed molecular dynamics simulation with respect to the first atomic assembly model after the energy minimization calculation, and equilibrated the first atomic assembly model.
- a simulation condition simulation time
- the control unit 12 caused the storage unit 13 to store data for the first atomic assembly model after the equilibration (coordinates of each of atoms constituting atomic assembly A, the kind thereof, a mass thereof, a partial charge thereof, interatomic bond information and the like).
- the kind of an atom means the kind of an element in the periodic table and an atomic type to designate a potential parameter(s) used in computer simulation.
- a condition for molecular dynamics simulation was set as follows.
- a periodic boundary condition was employed.
- the pressure condition the pressure was controlled to 1 atm by setting a keyword “langevinPiston” for the pressure control to on and setting “langevinPistonTarget” to 1.01325 in the input file of the NAMD program.
- the temperature condition the temperature was raised gradually by setting a keyword “langevin” for the temperature control to on and setting “langevinTemp” to a value of 50 Kelvin to 300 Kelvin every 50 Kelvin in the input file of the NAMD program.
- the each simulation time was 100 picoseconds at 50 Kelvin to 250 Kelvin, and was 1000 picoseconds at 300 Kelvin.
- a shake method was employed as a numerical solution of an equation of motion, and a time step was set to 2 femtoseconds.
- the output condition coordinates of the first atomic assembly model were output every 200 femtoseconds.
- a keyword “switching” for the switching function used for van der Waals potential and Coulomb potential calculation was set to 10 angstroms, and a keyword “cutoff” for the cut-off radius was set to 12 angstroms.
- PME particle mesh ewald
- an NPT ensemble was constituted by performing the temperature control and the pressure control mounted on the NAMD program.
- Step S 123 A Acquisition of Coordinates of Atomic Assembly A by Computer Simulation
- step S 123 A the control unit 12 caused the NAMD program to read data for the first atomic assembly model after the equilibration that is stored in the storage unit 13 (coordinates of each of atoms constituting atomic assembly A, the kind thereof, a mass thereof, a partial charge thereof, interatomic bond information and the like) and data for a simulation condition (simulation time, a temperature condition, a pressure condition, the kind of a potential parameter(s) and a value(s) thereof, the kind of an ensemble generated, a boundary condition, a numerical solution of an equation of motion, a time step of numerical integration, a switching function and a cut-off radius for van der Waals potential and Coulomb potential calculation, a condition for a long-distance interaction in Coulomb potential calculation, a 1-4 interaction, an output condition such as the number of snapshots and the like), and performed molecular dynamics simulation with respect to the first atomic assembly model after the equilibration.
- the kind of an atom means the kind of an element in the periodic
- a condition for molecular dynamics simulation was set as follows.
- a periodic boundary condition was employed.
- the pressure condition the pressure was controlled to 1 atm by setting a keyword “langevinPiston” for the pressure control to on and setting “langevinPistonTarget” to 1.01325 in an input file of the NAMD program.
- the temperature condition in an input file of the NAMD program, a keyword “langevin” for the temperature control was set to on, and “langevinTemp” was set to 300 Kelvin.
- the simulation time was 5000 picoseconds, a shake method was employed as a numerical solution of an equation of motion, and a time step was set to 2 femtoseconds.
- the output condition coordinates of the first atomic assembly model were output every 50 femtoseconds.
- a keyword “switching” for the switching function used for van der Waals potential and Coulomb potential calculation was set to 10 angstroms, and a keyword “cutoff” for the cut-off radius was set to 12 angstroms.
- PME particle mesh ewald
- an NPT ensemble was constituted by performing the temperature control and the pressure control mounted on the NAMD program.
- Step S 130 A Acquisition of Coordinates of Atomic Assembly AB
- step S 130 A the control unit 12 performed steps S 131 A to S 134 A.
- Step S 131 A Creation of Third Atomic Assembly Model
- Ligand L 1 formed of structure a and fragment B connected to the structure a was selected as atomic assembly C. In atomic assembly C, surrounding of ligand L 1 was in vacuum.
- step S 131 A the control unit 12 caused the NAMD program to read data for the third atomic assembly model stored in the storage unit 13 (coordinates of each of atoms constituting ligand L 1 , the kind thereof, a mass thereof, a partial charge thereof, interatomic bond information and the like) and simulation conditions for energy minimization calculation (the number of calculations of a force applied to each atom, the kind of a potential parameter(s) and a value(s) thereof, a boundary condition, a switching function and a cut-off radius for van der Waals potential and Coulomb potential calculation, a long-distance interaction in Coulomb potential calculation, a condition for a 1-4 interaction and the like), and performed energy minimization calculation with respect to the third atomic assembly model.
- the control unit 12 caused the NAMD program to read data for the third atomic assembly model stored in the storage unit 13 (coordinates of each of atoms constituting ligand L 1 , the kind thereof, a mass thereof, a partial charge thereof, interatomic bond information and the like)
- the control unit 12 caused the storage unit 13 to store data for the third atomic assembly model after the energy minimization calculation (coordinates of each of atoms constituting ligand L 1 , the kind thereof, a mass thereof, a partial charge thereof, interatomic bond information and the like).
- the kind of an atom means the kind of an element in the periodic table and an atomic type to designate a potential parameter(s) used in computer simulation.
- a condition of the energy minimization calculation is as follows.
- step S 131 A energy minimization calculation of ligand L 1 in vacuum was performed, and therefore the boundary condition and a condition for a long-distance interaction in Coulomb potential calculation was not particularly designated.
- the number of calculations of a force applied to each atom, in an input file of the NAMD program “minimize” was set to 1000.
- a keyword “switching” for the switching function used for van der Waals potential and Coulomb potential calculation was set to 10 angstroms, and a keyword “cutoff” for the cut-off radius was set to 12 angstroms.
- Step S 132 A Acquisition of Coordinates of Atomic Assembly C by Computer Simulation
- step S 132 A the control unit 12 performed molecular dynamics simulation with respect to the third atomic assembly model after the energy minimization calculation.
- a condition for molecular dynamics simulation was set as follows.
- a keyword “langevin” for the temperature control was set to on, and “langevinTemp” was set to 300 Kelvin.
- the simulation time was 10 nanoseconds, a shake method was employed as a numerical solution of an equation of motion, and a time step was set to 2 femtoseconds.
- coordinates of the third atomic assembly model were output every 100 femtoseconds, and 100000 sets of coordinates of atomic assembly C were generated.
- a keyword “switching” for the switching function used for van der Waals potential and Coulomb potential calculation was set to 10 angstroms, and a keyword “cutoff” for the cut-off radius was set to 12 angstroms.
- Step S 133 A Fitting of Coordinates of Atomic Assembly C with Respect to Coordinates of Atomic Assembly A in State F x
- step S 133 A the control unit 12 constituted 100000 sets of a pair Q (F 1 , H 1 ) formed of coordinates R A (F 1 ) of atomic assembly A and coordinates R C (H 1 ) of atomic assembly C, a pair Q (F 2 , H 2 ) formed of coordinates R A (F 2 ) of atomic assembly A and coordinates R C (H 2 ) of atomic assembly C, . . . , and a pair Q (F 100000 , H 100000 ) formed of coordinates R A (F 100000 ) of atomic assembly A and coordinates R C (H 100000 ) of atomic assembly C in total.
- control unit 12 While maintaining relative coordinates (internal coordinates) between each of atoms in coordinates of atomic assembly C for each of pairs Q (F 1 , H 1 ) to Q(F 100000 , H 100000 ), the control unit 12 performed fitting of atoms constituting a selected atomic group of atomic assembly C with respect to atoms constituting a selected atomic group of atomic assembly A using numerical formula (7), and superimposed atomic assembly C on atomic assembly A.
- Cn set for each atom in numerical formula (7) is as follows.
- Step S 134 A Acquisition of Coordinates of Atomic Assembly AB
- step S 134 A the control unit 12 acquired coordinates of fragment B contained in atomic assembly C (however, excluding coordinates of a point charge that is a virtual atom) from coordinates of atomic assembly C superimposed on atomic assembly A for each of pairs Q (F 1 , H 1 ) to Q(F 100000 , H 100000 ), added the coordinates to coordinates of atomic assembly A, and acquired coordinates R AB (F i ) of atomic assembly AB. Coordinates R AB (F 1 ) to R AB (F 100000 ) of atomic assembly AB were thereby acquired.
- Step S 140 A Calculation of Interaction Energy ⁇
- step S 140 A the control unit 12 calculated interaction energy ⁇ between structure a and fragment B connected to the structure a for each of coordinates R AB (F 1 ) to R AB (F 100000 ) of atomic assembly AB.
- the control unit 12 performed the following steps.
- E L1 (F i ) is an energy caused by an interaction between atoms of structure aB (ligand L 1 ), and an internal energy of ligand L 1 .
- E a (F i ) is an energy caused by an interaction between atoms of structure a, and an internal energy of structure a.
- E d (F i ) is an energy caused by an interaction between atoms constituting fragment B except for a virtual atom(s)
- EC d (F i ) is an energy caused by an electrostatic interaction between atoms constituting fragment B except for a virtual atom(s).
- EC f (F i ) is an energy caused by an electrostatic interaction between atoms constituting structure f.
- step S 150 A the control unit 12 created a histogram in which the horizontal axis indicated each class of interaction energy ⁇ and the vertical axis indicated a frequency in each class of interaction energy ⁇ .
- the class interval ⁇ was set such that the product of ⁇ and the frequency thereof H 0 ( ⁇ ) in each class interval ⁇ was constant, and the number of division of interaction energy ⁇ , that is, the number of class intervals ⁇ was set to 100.
- Step S 160 A Calculation of Appearance Probability P 0 ( ⁇ ) in Each Class of Interaction Energy ⁇
- step S 160 A the control unit 12 normalized the histogram created in step S 150 A, and calculated an appearance probability P 0 ( ⁇ ) in each class of interaction energy ⁇ .
- Step S 170 A Calculation of Interaction Energy ⁇
- the input unit 11 input various files required for calculation and created by using the gen structure program or the gen_input program as a part of the energy representation method program group such as parameter files, in the control unit 12 .
- the control unit 12 caused the storage unit 13 to store the input files.
- the energy representation method program group version 0.2.3 was used.
- a parameter(s) for van der Waals of an atom(s) constituting structure a was changed to zero.
- a partial charge(s) other than a partial charge(s) of an atom(s) constituting fragment B including a virtual atom(s) was changed to zero.
- each ⁇ w(i) is a set of 9492 interaction energy values between fragment B and each water molecule in total.
- Step S 180 A Creation of Frequency Distribution in Each Class of Interaction Energy ⁇ in Each Class of Interaction Energy ⁇
- the control unit 12 selected ⁇ p and ⁇ w calculated using coordinates belonging to each class of interaction energy ⁇ in the histogram created in step S 150 A from ⁇ p(1) to ⁇ p(100000) and ⁇ w(1) to ⁇ w(100000) calculated in step S 170 A, and created histograms H 0 ′( ⁇ p; ⁇ ) and H 0 ′( ⁇ w; ⁇ ) for the selected ⁇ p and ⁇ w.
- Step S 190 A Calculation of Appearance Probability P 0 ′( ⁇ ; ⁇ ) in Each Class of Interaction Energy ⁇ in Each Class of Interaction Energy ⁇
- the control unit 12 calculated appearance probabilities P 0 ′( ⁇ p; ⁇ ) and P 0 ′( ⁇ w; ⁇ ) in each class of the histograms H 0 ′( ⁇ p; ⁇ ) and H 0 ′( ⁇ w; ⁇ ).
- the histograms H 0 ′( ⁇ p; ⁇ ) and H 0 ′( ⁇ w; ⁇ ) and appearance probabilities P 0 ′( ⁇ p; ⁇ ) and P 0 ′( ⁇ w; ⁇ ) in steps S 180 A and S 190 A were created by the ermod program as a part of the energy representation method program group.
- H 0 ′( ⁇ p; ⁇ ) and the appearance probability P 0 ′( ⁇ p; ⁇ ) in creation of the histogram H 0 ′( ⁇ p; ⁇ ) and the appearance probability P 0 ′( ⁇ p; ⁇ ), in a parameter_er file in which parameters of the ermod program were input, setting of ecfbin and ec0bin was changed to 0.05, setting of engdiv was changed to 10, and setting of maxins was changed to 1 from a default condition.
- H 0 ′( ⁇ w; ⁇ ) and P 0 ′( ⁇ w; ⁇ ) were created by changing setting of engdiv to 10 and changing setting of maxins to 1 from a default condition.
- the control unit 12 performed steps S 180 A to S 190 A in each class of interaction energy ⁇ in the histogram created in step S 150 A, and calculated appearance probabilities P 0 ′( ⁇ p; ⁇ ) and P 0 ′( ⁇ w; ⁇ ) of interaction energy ⁇ for each class of interaction energy ⁇ .
- Step S 210 A Creation of Second Atomic Assembly Model
- Step S 220 A Acquisition of Coordinates of Atomic Assembly AB by Computer Simulation
- the acquired coordinates of atomic assembly AB were 100000 sets of coordinates R AB (G 1 ), R AB (G 2 ), . . . , and R AB (G 100000 ) in total.
- Step S 230 A Calculation of Interaction Energy ⁇
- step S 230 A the control unit 12 performed step S 230 A in a similar manner to step S 140 A, and calculated interaction energy ⁇ between structure a and fragment B connected to the structure a for each of coordinates R AB (G 1 ) to R AB (G 100000 ) of atomic assembly AB.
- Step S 240 A Creation of Frequency Distribution in Each Class of Interaction Energy ⁇
- step S 240 A the control unit 12 created a histogram in which the horizontal axis indicated each class of interaction energy ⁇ and the vertical axis indicated a frequency in each class of interaction energy ⁇ .
- Each class interval ⁇ was set to be the same as each ⁇ set in step S 150 A, and the number of division of interaction energy ⁇ , that is, the number of class intervals ⁇ was set to 100.
- Step S 250 A Calculation of Appearance Probability P( ⁇ ) in Each Class of Interaction Energy ⁇
- step S 250 A the control unit 12 normalized the histogram created in step S 240 A, and calculated an appearance probability P( ⁇ ) in each class of interaction energy ⁇ .
- Step S 260 A Calculation of Interaction Energy ⁇
- each ⁇ w(i) is a set of 9492 interaction energy values between fragment B and each water molecule in total.
- various files required for calculation were created, and the SltInfo file was changed in a similar manner to step S 170 A.
- Step S 270 A Creation of Frequency Distribution in Each Class of Interaction Energy ⁇
- step S 270 A the control unit 12 created histograms H′( ⁇ p) and H′( ⁇ w) for ⁇ p(1) to ⁇ p(100000) and ⁇ w(1) to ⁇ w(100000) calculated in step S 260 A.
- Step S 280 A Calculation of Appearance Probability P′( ⁇ ) in Each Class of Interaction Energy ⁇
- step S 280 A the control unit 12 calculated appearance probabilities P′( ⁇ p) and P′( ⁇ w) in each class of the histograms H′( ⁇ p) and H′( ⁇ w).
- the histograms H′( ⁇ p) and H′( ⁇ w) and appearance probabilities P′( ⁇ p) and P′( ⁇ w) in steps S 270 A and S 280 A were created by the ermod program as a part of the energy representation method program group.
- a parameter of the ermod program in creation of the histogram H′( ⁇ p) and P′( ⁇ p), in a parameter_er file in which a parameter of the ermod program was input, setting of ecfbin and ec0bin was changed to 0.05 from a default condition.
- H′( ⁇ w) and P′( ⁇ w) were created under a default condition.
- the control unit 12 calculated appearance probabilities P′( ⁇ p) and P′( ⁇ w) in each class of interaction energy ⁇ through steps S 260 A to S 280 A.
- Step S 300 A Calculation of Free Energy Change Amount ⁇ ( ⁇ )P( ⁇ )d ⁇ Caused by Interaction Energy ⁇
- Step S 300 A the control unit 12 calculated a free energy change amount ⁇ ( ⁇ )P( ⁇ )d ⁇ caused by interaction energy ⁇ through the following steps.
- the control unit 12 calculated ⁇ p( ⁇ )P( ⁇ )d ⁇ using an appearance probability P( ⁇ ) in each class of interaction energy ⁇ , calculated in step S 250 A, an appearance probability P 0 ′( ⁇ p: ⁇ ) in each class of interaction energy ⁇ p in each class of interaction energy ⁇ , calculated in step S 190 A, an appearance probability P′( ⁇ p) in each class of interaction energy ⁇ p, calculated in step S 280 A, and a slvfe program as a part of the energy representation method program group.
- the control unit 12 calculated ⁇ w( ⁇ )P( ⁇ )d ⁇ using an appearance probability P( ⁇ ) in each class of interaction energy ⁇ , calculated in step S 250 A, an appearance probability P 0 ′( ⁇ w: ⁇ ) in each class of interaction energy ⁇ w in each class of interaction energy ⁇ , calculated in step S 190 A, an appearance probability P′( ⁇ w) in each class of interaction energy ⁇ w, calculated in step S 280 A, and the slvfe program as a part of the energy representation method program group.
- the control unit 12 calculated a free energy change amount ⁇ ( ⁇ )P( ⁇ )d ⁇ caused by interaction energy ⁇ using self-energy (Eself) of fragment B, obtained as an output of the slvfe program, and ⁇ p( ⁇ )P( ⁇ )d ⁇ and ⁇ w( ⁇ )P( ⁇ )d ⁇ calculated above according to numerical formula (9).
- Eself is a value calculated as a correction term in the energy representation method when molecular dynamics simulation on which a periodic boundary condition is imposed is performed.
- ⁇ ( ⁇ ) P ( ⁇ ) d ⁇ ⁇ p ( ⁇ ) P ( ⁇ ) d ⁇ + ⁇ w ( ⁇ ) P ( ⁇ ) d ⁇ +E self (9)
- Step S 400 A Calculation of ⁇ G4a
- step S 400 A the control unit 12 calculated ⁇ G4a′ based on an appearance probability P 0 ( ⁇ ) in each class of interaction energy ⁇ , calculated in step S 160 A, an appearance probability P( ⁇ ) in each class of interaction energy ⁇ , calculated in step S 250 A, ⁇ ( ⁇ )P( ⁇ )d ⁇ calculated in step S 300 A, and numerical formula (1):
- ⁇ ⁇ ⁇ G ⁇ ⁇ ⁇ ⁇ P ⁇ ( ⁇ ) ⁇ d ⁇ ⁇ ⁇ + RT ⁇ ⁇ P ⁇ ( ⁇ ) ⁇ log ⁇ ( P ⁇ ( ⁇ ) P 0 ⁇ ( ⁇ ) ) ⁇ d ⁇ ⁇ ⁇ + ⁇ ⁇ ⁇ ⁇ v ⁇ ( ⁇ ) ⁇ P ⁇ ( ⁇ ) ⁇ d ⁇ ⁇ ⁇ ( 1 )
- R represents a gas constant
- T represents an absolute temperature (300 Kelvin) set in molecular dynamics simulation
- atomic assembly constituting ligand L 0 and water molecules present around the ligand L 0 before the change was referred to as “atomic assembly A”
- atomic assembly constituting ligand L 1 and water molecules present around the ligand L 1 after the change was referred to as “atomic assembly AB”
- a difference ⁇ G3a′ between the sum of free energy of atomic assembly A before the change and free energy of fragment B, and free energy of atomic assembly AB after the change was calculated based on numerical formula (1).
- ⁇ G3a is a free energy change amount regarding change represented by reaction formula (10).
- ⁇ G3a′ was calculated by performing steps S 110 B to S 190 B, S 210 B to S 280 B, S 300 B, and S 400 B corresponding to steps S 110 to S 190 , S 210 to S 280 , S 300 , and S 400 illustrated in FIG. 2 using the calculation device illustrated in FIG. 1 .
- steps S 121 B to S 123 B corresponding to steps S 121 to S 123 illustrated in FIG. 3 were performed.
- steps S 131 B to S 134 B corresponding to steps S 131 b to S 134 b illustrated in FIG. 5 were performed.
- steps S 221 B to S 223 B corresponding to steps S 221 to S 223 illustrated in FIG. 6 were performed.
- the input unit 11 input data for ligand L 0 contained in atomic assembly A before the change and ligand L 1 contained in atomic assembly AB after the change in the control unit 12 .
- the control unit 12 caused the storage unit 13 to store the input data.
- the input data was obtained by extracting data for ligand L 0 and ligand L 1 from data for complexes L 0 R and L 1 R used in calculation of ⁇ G4a, and coordinates data thereof exists in the three-dimensional structure files 3PTB_L 0 and 3PTB_L 1 , respectively.
- the input unit 11 input data for a simulation condition in the control unit 12 .
- the control unit 12 caused the storage unit 13 to store the input data.
- the input data was similar to that used in calculation of ⁇ G4a except for data for protein R.
- Step S 110 B Creation of First Atomic Assembly Model
- Step S 110 B the control unit 12 read the PDB file (3PTB_L 0 ) stored in the storage unit 13 using visualization software VMD, then generated 815 water molecules with gravity coordinates of atoms constituting ligand L 0 as an origin using the “solvate” function mounted on the VMD, created a rectangular type basic cell, and created the first atomic assembly model modeling atomic assembly A before the change.
- potential parameters of each atom CGenFF was used for each of atoms constituting ligand L 0 and ligand L 1
- TIP3P was used for each of atoms constituting water molecules.
- the potential parameters of each of atoms constituting ligand L 0 and ligand L 1 was determined using the MATCH program.
- Step S 120 B acquisition of atom of atomic assembly A by computer simulation
- Step S 130 B acquisition of coordinates of atomic assembly AB
- Step S 140 B calculation of interaction energy ⁇
- Step S 150 B creation of frequency distribution in each class of interaction energy ⁇
- Step S 160 B calculation of appearance probability P 0 ( ⁇ ) in each class of interaction energy ⁇
- Step S 170 B calculation of interaction energy ⁇
- Step S 180 B creation of frequency distribution in each class of interaction energy ⁇ in each class of interaction energy ⁇
- Step S 190 B calculation of appearance probability P 0 ′( ⁇ ; ⁇ ) in each class of interaction energy ⁇ in each class of interaction energy ⁇
- control unit 12 performed steps S 120 B to S 190 B in a similar manner to steps S 120 A to S 190 A.
- a condition for molecular dynamics simulation was similar to step S 120 A except that equilibration by gradual temperature rising was not performed, equilibration simulation whose temperature was set to 300 K and simulation time was set to 100 picoseconds was performed after energy minimization, and coordinates of atomic assembly A was output in a time step of 10 femtoseconds by setting simulation time after equilibration to 1000 picoseconds.
- Step S 210 B creation of second atomic assembly model
- Step S 220 B acquisition of coordinates of atomic assembly AB by computer simulation
- Step S 230 B calculation of interaction energy ⁇
- Step S 240 B creation of frequency distribution in each class of interaction energy ⁇
- Step S 250 B calculation of appearance probability P( ⁇ ) in each class of interaction energy ⁇
- Step S 260 B calculation of interaction energy ⁇
- Step S 270 B creation of frequency distribution in each class of interaction energy ⁇
- Step S 280 B calculation of appearance probability P′( ⁇ ) in each class of interaction energy ⁇
- control unit 12 performed steps S 210 B to S 280 B in a similar manner to steps S 210 A to S 280 A.
- a condition for molecular dynamics simulation was similar to step S 220 A except that equilibration by gradual temperature rising was not performed, equilibration simulation whose temperature was set to 300 K and simulation time was set to 100 picoseconds was performed after energy minimization, and coordinates of atomic assembly AB was output in a time step of 10 femtoseconds by setting simulation time after equilibration to 1000 picoseconds.
- Step S 300 B Calculation of Free Energy Change Amount ⁇ ( ⁇ )P( ⁇ )d ⁇ Caused by Interaction Energy ⁇
- Step S 400 B Calculation of ⁇ G3a
- control unit 12 performed steps S 300 B to S 400 B in a similar manner to steps S 300 A to S 400 A.
- atomic assembly constituting complex L 0 R and water molecules present around the complex L 0 R before the change was referred to as “atomic assembly A”
- atomic assembly constituting complex L 2 R and water molecules present around the complex L 2 R after the change was referred to as “atomic assembly AB”
- a difference ⁇ G4b between the sum of free energy of atomic assembly A before the change and free energy of fragment B, and free energy of atomic assembly AB after the change was calculated.
- ⁇ G4b was calculated by performing steps S 110 C to S 190 C, S 210 C to S 280 C, S 300 C, and S 400 C corresponding to steps S 110 to S 190 , S 210 to S 280 , S 300 , and S 400 illustrated in FIG. 2 using the calculation device illustrated in FIG. 1 .
- steps S 121 C to S 123 C corresponding to steps S 121 to S 123 illustrated in FIG. 3 were performed.
- steps S 131 C to S 134 C corresponding to steps S 131 b to S 134 b illustrated in FIG. 5 were performed.
- steps S 221 C to S 223 C corresponding to steps S 221 to S 223 illustrated in FIG. 6 were performed.
- a chemical structure of ligand L 2 is as follows.
- a partial charge of each of atoms constituting ligand L 2 is as follows.
- fragment B is as follows.
- Steps S 110 C to S 190 C, S 210 C to S 280 C, S 300 C, and S 400 C were performed in a similar manner to steps S 110 A to S 190 A, S 210 A to S 280 A, S 300 A, and S 400 A in calculation of ⁇ G4a except that ligand L 1 was changed to ligand L 2 and fragment B was changed.
- the calculated ⁇ G4b was ⁇ 17.84 (kcal/mol).
- atomic assembly constituting ligand L 0 and water molecules present around the ligand L 0 before the change was referred to as “atomic assembly A”
- atomic assembly constituting ligand L 2 and water molecules present around the ligand L 2 after the change was referred to as “atomic assembly AB”
- a difference ⁇ G3b between the sum of free energy of atomic assembly A before the change and free energy of fragment B, and free energy of atomic assembly AB after the change was calculated.
- ⁇ G3b was calculated by performing steps S 110 D to S 190 D, S 210 D to S 280 D, S 300 D, and S 400 D corresponding to steps S 110 to S 190 , S 210 to S 280 , S 300 , and S 400 illustrated in FIG. 2 using the calculation device illustrated in FIG. 1 .
- steps S 121 D to S 123 D corresponding to steps S 121 to S 123 illustrated in FIG. 3 were performed.
- steps S 131 D to S 134 D corresponding to steps S 131 b to S 134 b illustrated in FIG. 5 were performed.
- steps S 221 D to S 223 D corresponding to steps S 221 to S 223 illustrated in FIG. 6 were performed.
- Steps S 110 D to S 190 D, S 210 D to S 280 D, S 300 D, and S 400 D were performed in a similar manner to steps S 110 B to S 190 B, S 210 B to S 280 B, S 300 B, and S 400 B in calculation of ⁇ G3a except that ligand L 1 was changed to ligand L 2 and fragment B was changed.
- the calculated ⁇ G3b was ⁇ 14.91 (kcal/mol).
- ⁇ G determined by an experiment described in published literatures (Journal of Chemical Theory and Computation, 8, 3686-3695 (2012) and Journal of the American Chemical Society, 99, 2331-2336 (1977)) is ⁇ 0.10 (kcal/mol).
- ⁇ G determined by a calculation method had a difference of 1 kcal/mol or less from the ⁇ G determined by an experiment, and was in good agreement therewith.
- ⁇ G was calculated in a similar manner to Example 1 using ligand L 3 in place of ligand L 2 .
- a chemical structure of ligand L 3 is as follows.
- a partial charge of each of atoms constituting ligand L 3 is as follows.
- fragment B is as follows.
- ⁇ G was calculated in a similar manner to Example 1 by handling a point charge (partial charge; 0.000) as an atom constituting fragment B for convenience.
- the calculated ⁇ G3b was ⁇ 5.45 (kcal/mol).
- the calculated ⁇ G was ⁇ 0.08 (kcal/mol).
- ⁇ G determined by an experiment described in published literatures (Journal of Chemical Theory and Computation, 8, 3686-3695 (2012) and Journal of the American Chemical Society, 99, 2331-2336 (1977)) is 0.27 (kcal/mol).
- ⁇ G determined by a calculation method had a difference of 1 kcal/mol or less from the ⁇ G determined by an experiment, and was in good agreement therewith.
- ⁇ G was calculated in a similar manner to Example 1 using ligand L 4 in place of ligand L 2 .
- a chemical structure of ligand L 4 is as follows.
- a partial charge of each of atoms constituting ligand L 4 is as follows.
- fragment B is as follows.
- the calculated ⁇ G4b was ⁇ 23.00 (kcal/mol).
- the calculated ⁇ G3b was ⁇ 19.88 (kcal/mol).
- the calculated ⁇ G was ⁇ 0.53 (kcal/mol).
- ⁇ G determined by an experiment described in published literatures (Journal of Chemical Theory and Computation, 8, 3686-3695 (2012) and Journal of the American Chemical Society, 99, 2331-2336 (1977)) is ⁇ 0.40 (kcal/mol).
- ⁇ G determined by a calculation method had a difference of 1 kcal/mol or less from the ⁇ G determined by an experiment, and was in good agreement therewith.
- ⁇ G was calculated in a similar manner to Example 1 using ligand L 5 in place of ligand L 2 .
- a chemical structure of ligand L 5 is as follows.
- a partial charge of each of atoms constituting ligand L 5 is as follows.
- fragment B is as follows.
- ⁇ G was calculated in a similar manner to Example 1 by handling a point charge (partial charge; 0.000) as an atom constituting fragment B for convenience.
- the calculated ⁇ G3b was 3.55 (kcal/mol).
- ⁇ G determined by an experiment described in a published literature (Journal of the American Chemical Society, 125, 10570-10579 (2003)) is 0.93 (kcal/mol).
- ⁇ G determined by a calculation method had a difference of 1 kcal/mol or less from the ⁇ G determined by an experiment, and was in good agreement therewith.
- ⁇ G was calculated in a similar manner to Example 1 using ligand L 6 in place of ligand L 2 .
- a chemical structure of ligand L 6 is as follows.
- a partial charge of each of atoms constituting ligand L 6 is as follows.
- fragment B is as follows.
- ⁇ G was calculated in a similar manner to Example 1 by handling a point charge (partial charge; 0.000) as an atom constituting fragment B for convenience.
- the calculated ⁇ G4b was ⁇ 3.79 (kcal/mol).
- the calculated ⁇ G was ⁇ 0.25 (kcal/mol).
- ⁇ G determined by an experiment described in a published literature (Journal of the American Chemical Society, 125, 10570-10579 (2003)) is 0.25 (kcal/mol).
- ⁇ G determined by a calculation method had a difference of 1 kcal/mol or less from the ⁇ G determined by an experiment, and was in good agreement therewith.
Abstract
Description
A+B→AB (1)
A+B→AB (1)
A+B→AB (1)
- 1 calculation device
- 11 input unit
- 12 control unit
- 12A first atomic assembly model creation unit
- 12B first coordinates acquisition unit
- 12C second coordinates acquisition unit
- 12D first interaction energy ϕ frequency distribution creation unit
- 12E first interaction energy ϕ appearance probability calculation unit
- 12F first interaction energy ε frequency distribution creation unit
- 12G first interaction energy ε appearance probability calculation unit
- 12H second atomic assembly model creation unit
- 12I third coordinates acquisition unit
- 12J second interaction energy ϕ frequency distribution creation unit
- 12K second interaction energy ϕ appearance probability calculation unit
- 12L second interaction energy ε frequency distribution creation unit
- 12M second interaction energy ε appearance probability calculation unit
- 12N ∫Δν(ϕ)P(ϕ)dϕ calculation unit
- 12O ΔG calculation unit
- 13 storage unit
- 13A data for atomic assembly A before the change
- 13B data for first simulation condition
- 13C first simulation program
- 13D data for atomic assembly AB after the change
- 13E data for second simulation condition
- 13F second simulation program
- 14 output unit
δ(ϕ−(Ξ(ψ,K)−Ψ(ψ)−W(K)))
is a delta function of Dirac, and is a function to obtain 1 when ϕ is equal to
Ξ(ψ,K)−Ψ(ψ)−W(K)
and to obtain zero when ϕ is not equal thereto.
A+B→AB (1)
ϕ(F i)=E L1(F i)−E a(F i)−E B(F i) (8).
Step S150A: Creation of Frequency Distribution in Each Class of Interaction Energy ϕ
∫Δν(ϕ)P(ϕ)dϕ=∫Δνp(ϕ)P(ϕ)dϕ+∫Δνw(ϕ)P(ϕ)dϕ+Eself (9)
Step S400A: Calculation of ΔG4a
ΔΔG=ΔG4−ΔG3,
ΔG4=ΔG4a+ΔG4b, and
ΔG3=ΔG3a+ΔG3b
Claims (15)
A+B 1 →AB 1 (1-1)
A+B 2 →AB 2 (1-2)
A+B 1 →AB 1 (1-1)
A+B 2 →AB 2 (1-2)
A+B 1 →AB 1 (1-1)
A+B 2 →AB 2 (1-2)
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WO2016052662A1 (en) | 2016-04-07 |
EP3203401A4 (en) | 2018-08-08 |
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US20170220717A1 (en) | 2017-08-03 |
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